Odemwingie headed the winner in the 2-1 victory which saw his side move into fourth place in the Premier League, just a point behind Roberto Di Matteo's Chelsea.
The Baggies have lost just once at home in the league so far this season and the Nigerian striker believes that Saturday's result will go a long way to proving some of their doubters wrong.
"It wasn't our best game but it was the best three points of the season because a good test came in the later stages where we needed to take away all the doubts about our great start," said Odemwingie.
"It was a good time to win against a big club in November, to show that after we beat teams like Liverpool and Everton and got an away point at Tottenham, that we're still on the same upward movement.
"It definitely gives us great belief. Our results have already given us confidence and the belief is growing but we need to keep putting things in there to keep us confident.
"The good thing is I think we are all improving. Players look more ambitious and in games you feel like you are alongside players who have confidence that they are good."
He was also full of praise for his strike partner Shane Long, who scored the opener and set up Odemwingie's winner despite the death of his grandmother just a day before the game.
Odemwingie added: "I didn't know what had happened until after the game. I wondered why Shane was a bit quiet. After the match we were celebrating with some music in the dressing room and he wasn't with us, but I didn't want to ask what happened.
"I asked him 'are you not happy with the assist?' and he didn't tell me what happened. But now it is clear and he deserves all the respect for playing because it was a big game for us and he played very well. A lot of credit to him for that."