England drew 0-0 with Slovakia in their final group match after Hodgson decided to leave England's record scorer on the bench.
Jordan Henderson replaced Rooney in midfield with Nathaniel Clyne and Ryan Bertrand taking over from Tottenham full-backs Kyle Walker and Danny Rose.
Dele Alli was also dropped for an out-of-form Jack Wilshere, while Raheem Sterling and Harry Kane were replaced by Jamie Vardy and Daniel Sturridge.
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Rooney was introduced midway through the second half for Wilshere, but England could not find the goal they needed.
They finished second behind Wales in Group B before they crashed out in the last 16 to Iceland before Hodgson resigned as manager.
"I felt we had a good squad," said Rooney, speaking to the Daily Mail.
"A lot of ability, a lot of talent. Yes, we had some young lads and you know there is a risk some won't react as positively at a tournament, but I still thought we could do really well. To then go out as we did, and against Iceland, was beyond disappointing.
"If you leave playing your best, beaten by a better team, I accept that. But we didn't play. We had lost momentum from the Slovakia game and tournament football is about confidence. You get that from winning.

Hodgson quits, Iceland boss vows 'we can beat anyone'

"It was Roy's decision to make those changes against Slovakia and either way, the team he put out should have been able to win. But, right or wrong, I wanted to play and I can't deny that."
"I wouldn't have rested six players," he said. "It's more than half the team. It was a gamble and it didn't pay off.
"When I came on against Slovakia it was difficult to change the game, impossible really. I was running around just trying to get the energy back into the team."

Did Roy get it wrong?

Yes, says former England defender Paul Parker - England's doom masterminded by Hodgson, a manager who had to go because his decisions were appalling
The former England full back adds: "There was also another big problem in Hodgson's approach: his ludicrous decision to rest a load of players in the final group stage match. This is something that drives me absolutely mad: there are guys out there digging up roads every day from six in the morning til six at night, and you're trying to tell me that a professional footballer isn't capable of playing two 90-minute football matches five or six days apart?
"I've a little sympathy for Hodgson in that this is one of those things that modern coaches feel they need to do. But what about Gary Neville standing alongside him? This is a man who knows everything there is to know about the importance of momentum, and the winning mentality; he must have known that keeping the same team together would have helped England no end. So why didn't he press the case with Roy?"
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