Toffees boss Koeman admitted his team under-performed in the 3-1 loss at Anfield and accepted the pair could have played better.
But the Dutchman felt it was unfair for Barkley and Lukaku to be singled out.
Speaking to reporters ahead of Tuesday's Premier League trip to Manchester United, Koeman said: "What I don't like is too much individually about the performances of the players because it is a team, every individual is part of the team and the team was not good enough.
Liverpool 3 Everton 1 player ratings
Liverpool 3 Everton 1 player ratings
1/22 Simon Mignolet – 6 out of 10
Made a handful of important saves – only beaten by Pennington’s close range strike.
2/22 Nathaniel Clyne – 5 out of 10
Was pulled out of position at times and made a habit of playing very narrow.
3/22 Joel Matip – 6 out of 10
His work rate was relentless and he kept Lukaku out of the game.
4/22 Dejan Lovren – 7 out of 10
Committed to every challenge and loose ball – courageous defending throughout.
5/22 James Milner – 6 out of 10
It was a classic Milner display – passed well, held his shape and worked hard.
6/22 Emre Can – 4 out of 10
Ruthlessly crashed into challenges, tackled half-heartedly and lost possession continuously.
7/22 Lucas – 6 out of 10
Read the game very well – dropped deep and opened up space in the midfield.
8/22 Georgino Wijnaldum – 5 out of 10
Drifted in and out of the game at times, but in possession he showed impressive vision and ability.
9/22 Sadio Mane – 7 out of 10
His opening goal was an example of his endless individual ability. Subbed off due to ankle injury.
10/22 Roberto Firmino – 6 out of 10
Worked hard to win possession, but his final product was sloppy at times.
11/22 Philippe Coutinho – 8 out of 10
Was Liverpool’s best player today – he was energetic, determined and his goal capped off a sublime performance.
12/22 Joel Robles – 4 out of 10
Was a victim of Liverpool’s sublime strike force but seemed out of position for all three of the home side's goals.
13/22 Matthew Pennington – 6 out of 10
Unexpectedly scored the equaliser, but then he was beaten by Coutinho for Liverpool’s second.
14/22 Ashley Williams – 6 out of 10
Tackled relentlessly and made countless clearances. However, some of his tackles looked dangerous.
15/22 Phil Jagielka – 7 out of 10
He cleared shots off the line, leaped in front of shots and saved the Everton side on numerous occasions.
16/22 Mason Holgate – 5 out of 10
Showed glimpses of brilliance going forward, but his countless deliveries into the box were over hit and out of control.
17/22 Tom Davies – 6 out of 10
Oozed with confidence and once again proved his prospects for the future. Still has plenty to learn, though.
18/22 Idrissa Gueye – 6 out of 10
Was a key element to Everton going forward, but he did drift out of position at times.
19/22 Leighton Baines – 5 out of 10
Played very deep, which resulted in a lack of width and menace for The Toffees on the front foot.
20/22 Ross Barkley – 6 out of 10
Should have been red carded just before the interval, but his performance improved sufficiently as the game progressed.
21/22 Romelu Lukaku – 4 out of 10
Showed no sign of being the Premier League’s scorer and caused few problems for the Liverpool defence.
22/22 Dominic Calvert-Lewin – 5 out of 10
Lacked service from the midfield, but the striker was invisible at times.
"I said not too much individually but maybe some players didn't perform at the level what maybe they showed in the last few games. Maybe, yes.
"Romelu, it was difficult. I spoke to Romelu, he was not really sharp, he was a little bit tired.
"(But) he's the top-scorer of the league. Why now about the Liverpool game (do) we need to criticise Rom? He's a great striker, he's working hard. It's a human boy, it's not always a 10, that's football and if you don't play football, maybe you don't understand it."
Moving on to England midfielder Barkley, Koeman added: "Ross played in a little different position than he played in the last few weeks. Of course, he lost several balls in the midfield, instead of playing a little bit faster and no dribbling with the ball.
"He needs to improve in that, but not to take out one or two (players for criticism) and that was the problem last Saturday, that's not fair.
"It's easy to give your opinion in front of the television without any responsibility. I'm happy, I see a lot of progress in the club, in the team, it's a whole season, it's not one game."
Seventh-placed Everton can move above their opponents with victory at Old Trafford.
Koeman expects a tough match, despite United's struggles in front of their home fans this season.
"We know that they have difficulties at home, maybe in the last few home results, but they had a lot of ball possession and were the better team in every game," he added. "They had chances to score.
"They are still a really strong team."