Stoke striker Crouch, who has scored 22 times in 42 appearances for England, was angry that he was not in the initial 23-man squad for Poland and Ukraine.
Boss Hodgson said: "I did try to sign him at Fulham. I selected him for the Euros as well but he didn't want to come.
"He was on a standby list but made it clear that, unless he was in the squad, he did not want to be considered.
"As a result, we've selected squads since that time when I felt I didn't need him in there.
"I'm not going to bring him in to fill up the bench.
"The day Crouch gets into an England squad is when I think he should be in the original 23.
"It's wrong to compare the type of players we're bringing in as a contingency plan."