The 62-year-old singer died from kidney failure last month after fighting cancer and pneumonia and suffering from a serious bowel condition.
Barry, the sole surviving member of the Bee Gees trio, had a trembling voice as he told the congregation at St Mary's Church in Thame, Oxfordshire: "Life is too short. In Robin's case, absolutely too short.
"We should have had 20 years, 30 years of his magnificent mind and his beautiful heart."
Referring to the late Maurice Gibb, he added: "They were both beautiful. And now they're together. They're actually together."
Maurice died in 2003.
Barry Gibb said: "When you're twins, you're twins all your life. You go through every emotion.
"And they're finally together. I think the greatest pain for Robin in the past 10 years was losing his twin brother, and I think it did all kinds of things to him.
"And now they're together."
Gibb's elderly mother, Barbara, left the church just before Barry - the last of the four Gibb brothers - gave his eulogy.
He told the congregation: "This is a very strange experience, having already lost two brothers and now Rob.
"I think there are an awful lot of things happening right now that maybe you won't be aware of. And one is how many people came on such a terrible day. It is staggering.
"So many people loved this boy, so many illustrious people are here that loved him. And that is such a pleasure to witness.
"The three of us have seen a lot of crowds but I've never seen so
much love in one crowd as I'm looking at today - for Rob, you know, for
the music. And it's an intense experience for me.
"I think it's an experience none of us will forget. We will keep him in our hearts and minds forever."
Mourners wept as Robin's ornate white coffin entered the church to the sound of the Bee Gees' hit How Deep Is Your Love.
Barry Gibb and the vicar leading
the service, the Reverend Alan Garratt, walked up the aisle ahead of it
as a round of spontaneous applause broke out from well-wishers outside the church.
Close relatives, including Robin's widow, Dwina, and his mother followed behind. One woman was so overcome with grief she had to be physically supported as she walked to her seat.
Barry told the congregation of his brother's sense of humour. He said their favourite television programme was The Goons, and added: "There was no funnier man than Spike Milligan - apart from Robin. And his sharp, intuitive wit will live with us forever.
"You could stand Robin next to Spike Milligan and it would be a competition."
He hinted at recent tensions between himself and Robin, however, saying: "We were laughing all the way. Sometimes crying. God knows how much we argued.
"Even right up to the end we found conflict with each other, which now means nothing. It just means nothing.
"If there's conflict in your lives - get rid of it."
Hundreds of well-wishers lined the streets of Thame ahead of the service to see the coffin in a horse-drawn hearse.
Onlookers watched as the white, glass-sided carriage - topped with red roses and pulled by four plumed, black Friesian horses - trundled through his adopted home town.
The cortege was followed by his two Irish wolfhounds, Ollie and Missy, together with friends and family.
In keeping with his long musical career, the horses wore decorative black cloths emblazoned with a gold treble clef and were trailing a piper.
It had been Robin's wish to "say a final goodbye to fans and his home town of Thame", according to his family.
Guests, including Sir Tim Rice, DJ Mike Read and Uri Geller, followed the cortege on foot from the gatehouse of his estate.
Joining funeral directors as pallbearers, were Robin's sons RJ and Spencer, together with Stevie Gibb - Barry's son - and Steven Murphy, who is Dwina's son.
Guests at the service were issued with an order of service printed with a black and white picture of Robin on the front cover, and images of red roses throughout.
An image of the three members of the Bee Gees was on the back.
Their younger brother Andy, who also had a chart career, died in 1988.
During the service Dwina read a poem called My Songbird Has Flown.
It included the words: "My songbird has flown and my soul sighs - but he will never go away."
She was embraced by Barry as she returned to her seat.
The poem was followed by a recording of Don't Cry Alone - one of Robin's last compositions, from his Titanic Requiem, which premiered just weeks before his death.
Guests left the church to the sound of the Bee Gees' song I Started A Joke, which includes the line "I finally died, which started the whole world living".
In his eulogy, Spencer had referred to the song, saying: "Dad, please know - it's your light, your words that will keep the whole world
living.
"I hope you can see that the joke was not on you."
Spencer told guests his father was "an incredibly complex man" who could "make you laugh in the most depressing of circumstances".
He said he was "someone who constantly looked forward to change and the future who still ate the same thing for breakfast every day".
He added: "The cream always rises to the top, he used to say. Dad, I think it's safe to say you achieved that over and over again.
"I will always be humbled by my father's voice and his talent - I think we all will."
Robin's young daughter Snow, whose mother is a former housekeeper of his, did not attend the service - but was mentioned by Barry at the end of his eulogy as "little Snow" in a list of close family members.
Barry had written a poem for his brother - which he called Ode To Rob.
It included the lines: "We will all be together one day. So fly away Rob, fly away. But knowing Rob, he will always be near.
"So today is tonight and the winter's our summer, and the end of the rainbow is here.
"You will always be with us. Let us celebrate his life, as he would want us to do.
"I love you Rob and always will."
There was also laughter during his tribute, as he recalled the Bee Gees' early days in Australia, where they were billed as a cabaret act, the Bee Gees Comedy Trio.
Chuckling, he told how Maurice and Robin were so small in comparison to him that they had to stand on tea chests during their first television appearance - "so they could get us all in the same picture".
The three brothers had "an obsession" with having their records played on the radio, the congregation heard, and would stay up until 3am
just to listen to their own songs.
RJ, the only child Robin and Dwina had together, told guests during his own eulogy: "My father, Robin Hugh Gibb, was a true Renaissance man.
"A man who saw excellence in the arts and had a wit and personality above and beyond anything or anyone I will encounter again.
"He was my truest friend, confidant, and as a father... well, I don't think a son could ever wish for any better."
RJ seemed close to tears as he addressed his late father, saying: "I will never forget the way you smiled with your eyes.
"Goodbye, my dearest father.
"I will love you always and will take comfort that you are always
only a song away, as I will surely hear your voice wherever I go.
"I will never be able to thank you enough for my upbringing and I will never forget the time we spent together.
"My best friend. My daddy. I love you so much. You were a brilliant light and a true inspiration to myself and to us all."
He walked to the coffin and gave it a tender kiss when he finished speaking.
Robin's daughter Melissa was too upset to read her tribute, with her brother Spencer giving it on her behalf.
In it, she said: "To my dad. I have only to say that I was proud of you.
"You are a soldier, fighting a battle to the end. How brave you are. You are a special angel and God knows that.
"Thank you for your love, laughter and for never judging me."
The church is opposite the home the musician shared with Dwina for 19 years.
The vicar told the congregation that flowers "filled the chapel" at the house, having been sent by loved ones after Robin's death.
He added that the hymns chosen for today's funeral were all favourites of Robin, who was later buried in the churchyard.
A memorial service is to take place at a later date.
Mr Garratt said of that occasion: "No doubt much will be said and brought to mind.
"Not just about his public persona and his wonderful musical career but also about the hidden generosity of spirit, hidden away from the camera and the spotlight."
PA
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