Rooney, who was banned for the first two games of the tournament, was not at his best against Ukraine and Italy, who beat the Three Lions on penalties in the quarter-finals.
That has led some to blame Rooney for England's failure to progress further, but Gerrard believes the Manchester United striker is judged by higher standards than the rest of the squad.
Gerrard said in The Sun Sunday: "I just think that ever since Wayne has been around, and because of his performances in Euro 2004, there is an expectation that he comes to these tournaments and wins them all on his own.
"I just think that's unfair - especially when it goes wrong and people then point to Wayne and his performances and blame him.
"But the responsibility has to be on all 23 players.
"It's unfair to look at Wayne and say because he didn't play well it's the reason why we haven't won.
"I've mentioned on many occasions that at this level the biggest thing is to play without expectation, without fear.
"So it's only normal that at times Wayne is brought down because of that expectation, because everyone expects and wants him to do well."
Meanwhile, former England striker Alan Shearer has warned he believes the team is going backwards.
Shearer is baffled by the praise Roy Hodgson's men received for their battling performances at the tournament in Poland and Ukraine.
He told The Sun Sunday: "If we accept this level of performance, then we have given up on England.
"Have we dropped so far down the pecking order that we are applauding England for trying hard and being well-organised?"
He continued: "I cannot remember the last time the nation celebrated the team getting out of our group.
"That used to be the least that was expected. Now it seems to be a pointer that we are heading in the right direction.
"Well, we are not. We are getting progressively worse if you look at our performances in the last three major tournaments we qualified for."