The captain opened the score in the side’s 4-0 Europa League home win over Feyenoord to take his tally to 39 United goals in continental competitions, one ahead of former striker Ruud van Nistelrooy.
Rooney’s first-half chip also moved him to 248 goals for the club overall, just one behind their all-time top scorer Sir Bobby Charlton.
The 31-year-old impressed for United on Thursday night, scoring one and assisting Juan Mata for the side’s second with an incisive reverse pass inside the Feyenoord box.
United striker Ibrahimovic, who set Rooney up for his goal in Thursday's match, said: "I think when you're famous like that, people are interested, they want to know everything.
"I don't know what has happened, I didn't even ask him because it's not important for me and I'm 100 per cent sure the media doesn't know what really happened.
"I think we should appreciate him for the player he is, what he did. I don't see many players from England who have had the same career as him.
"I feel a little bit sorry of the situation because we should show more respect for him. Everybody wants to make a little thing a big thing."
Ibrahimovic added of Rooney: "As a person he's fantastic. As a player, he's the perfect player.
"I'm happy for him to break the record and I will help him to go one more - then I see it as the real record."
His performance comes in the wake of a difficult period for the England international who was recently subject to wide scrutiny after appearing worse for wear during the recent international break, with Rooney reported to have been up until the early hours at a wedding at The Grove hotel.
Having subsequently issued a public apology over the "inappropriate" pictures, Rooney then last weekend labelled the way he has been treated by the media as "disgraceful".
After the Feyenoord game he hit out again, suggesting "people in the media (are) making a big deal over nothing" and claiming he "didn't even step foot into the wedding".
Rooney was asked afterwards if his goal was made even more satisfying by the recent furore.
He replied: "No. All that's created by people like yourself asking questions now, people in the media making a big deal over nothing.
"I actually didn't even step foot into the wedding and I think it's a shame that I'm having to talk about it now after such a great victory."
He added on BT Sport 2: "It's a great feeling to score goals and to score goals for this club. I'm sure there's plenty more to come."
United boss Jose Mourinho said of Rooney's European record: "It is an amazing achievement obviously and will be even better if he can help to bring to the club the only competition they have never won in their history, which is the Europa League. His performance was like the team - good, solid."