Cole swooped for the winner against Bolton Wanderers on the weekend and Hodgson can sense a new bounce in the player's step.
The former Fulham chief said: "The goal will do a lot for him, but he's quite confident at the moment.
"Joe is a very confident player. He always thinks he is playing well, so he doesn't have any great worries about that side of things.
"But, of course, one of the things he knows he will be criticised for, I guess, is that he doesn't score enough goals.
"If we think of his time here at Liverpool, we can all think of goal chances which were there to be taken which he didn't.
"So I'm sure he is delighted to have put that behind him by scoring a very, very important winning goal against Bolton."