The 30-year-old Manchester United midfielder was omitted from the 23-man party which was officially confirmed on Wednesday.
It was revealed that Carrick did not want to be considered if he was not pushing for a starting role with the Three Lions.
"We were advised a few months ago that because of where he was in his career, that he wanted to step back from being called up and sitting on the subs bench. He will help in extreme situations," confirmed the FA's Adrian Bevington.
Hodgson added: "I wouldn't dream of putting Michael Carrick on a standby list after he's made it clear in the past he doesn't want to be involved like that.
"I'd have to be convinced he was better than the four [central midfielders] I've selected, and that he'd be happy to come out of retirement."
Hodgson has instead named Liverpool's Jordan Henderson on his stand-by list and is happy with him.
"He's got great potential," he said.
"His recent matches have been very good in the centre of midfield and, in the future, he'll play there. He has potential in that area, tremendous athleticism, great box-to-box ability."
Henderson could get a call if Scott Parker does not recover from his Achilles injury - but Hodgson is confident he will be fine.
"He hasn't played because he's been resting the Achilles injury," said the boss.
"It was decided on Monday that he'd have this injection. From what I'm hearing, it won't be a problem. He's very confident, I'm confident, but I can't give a guarantee."
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