Hodgson has reassured Odemwingie of his importance at club level after he came off the bench to score the second goal in a 2-0 win.
Odemwingie said: "The coach (Hodgson) said he wasn't sure from the Monday beforehand that I would play in the Wolves game.
"I came back (from Nigeria) with a little bit of a cough and cold and didn't train for five days.
"I was disappointed because the derby is a game you want to play in because if you do well for the club and for the fans you are the man.
"But I saw the reasons for what he said and he encouraged me. He said I should remove all the doubts about myself.
"He said: 'All I should know is that I am one of the players that counts, that I was good and I shouldn't doubt anything'.
"That was a lift and after my goal all of my team-mates came running to and saying: 'You deserve this'. That really lifted me up."