Head coach Hodgson was aware of the pressure on Rooney to perform at his best after returning from a two-match ban for his sending off against Montenegro in a qualifying game last October.
But, after scoring the winner against Ukraine, Rooney was below par in the quarter-final defeat by Italy in Kiev on Sunday night when England were beaten 4-2 on penalties after a goalless 120 minutes.
Hodgson said: "I think we put a lot of expectations on Wayne.
"When he missed the first two games, we were all believing that what we needed to do was to get to the third game and Wayne Rooney will win us the championships.
"That maybe was too much to ask of him.
"Wayne certainly tried very hard, but he didn't have his best game. I think he would admit that."
But Hodgson conceded it was natural for the onus to be on the top players to perform on the biggest stages.
He said: "Do we put too much expectation on Rooney? Well we do, but so do other teams with their players, don't they?
"I think had (Andrea) Pirlo played poorly, it might have affected the Italians' performance.
"I think in all top international teams, you're looking at one, two, possibly three individuals that everyone recognises as being exceptional world-class talents.
"When you get to the big stage, you're hoping those players perform and show they're world-class talents, like the Maradonas that win Argentina a World Cup with his performance."
Rooney went on holiday in Las Vegas at the end of the domestic season and was pictured at a nightclub until the early hours.
But Hodgson was adamant Rooney was fit and up to speed in training sessions even though his only action in six weeks before returning against Ukraine was as a second-half substitute against Belgium.
When asked if the Las Vegas trip was ideal, Hodgson said: "Well, we haven't noticed anything with his fitness levels. We've monitored his fitness levels and in training he has looked very fit.
"In the first game (against Ukraine) he didn't show any particular signs of lacking any fitness and he played the 120 minutes.
"I think what you might be saying is that you're a bit disappointed with his performance and maybe thought he could have played better.
"It's not necessarily related to this (Rooney's fitness). You could put fitness down to anything. That was the classic Italian trick. Every time an Italian team loses a game, you hear they're not fit.
"You can put a lot of things down to fitness, but there was no reason for us to doubt his fitness. His running stats in the training sessions and the games were actually very good."
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