Hodgson and the squad have faced criticism for their displays in two defeats in Brazil, with their failure being confirmed on Friday when Costa Rica beat Italy, but Hart was eager to give the manager his backing.
"Me personally, I speak for the players when I say we are proud to play for Roy Hodgson," the Manchester City shot-stopper told members of the media.
"He is a great manager, a very passionate man, and someone I have an awful lot of respect for. I hope to continue playing for him.
"We haven't scored enough goals and let too many in. We are going to dissect it but we have committed our lives to this tournament, thrown everything we can at it."
England finish their Group D campaign against Costa Rica on Tuesday.