Odemwingie scored the winning goal in the Baggies' 2-1 success which propelled them into fourth spot in the Barclays Premier League and only one point behind Roberto Di Matteo's team.
It was their sixth home win in seven games but the Nigeria international feels toppling one of the division's big guns was a significant step forward.
Odemwingie said: "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.
"We needed to show people against a big club that we have started well but we want to continue that way, so it was the best three points of the season.
"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 that 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 you are alongside players who have confidence that they are good."
Baggies boss Steve Clarke has been able to rotate players with Odemwingie left out of the previous match against Wigan despite scoring both goals in the win over Southampton.
Then on Saturday the absence of Ben Foster, Gareth McAuley and Romelu Lukaku was hardly noticed as replacements Boaz Myhill, Gabriel Tamas and Odemwingie filled the gaps.
Odemwingie said: "Before the game, the manager made an extra comment on those who are not even on the bench.
"He said he needs everyone because there will be consecutive games in quick succession coming up.
"He said from the stands to the bench is not far and from the bench to the pitch isn't far.
"He has to manage that in a long season where we're hoping to achieve something. We need every player.
"It's normal that sometimes you ask questions (if you're not playing) but in the end it is the result that matters - and there are no questions because the result is there.
"I wanted to play after Southampton when I scored twice. I wanted to start again and I didn't start but we won, so what can I say?
"He is the manager and he decides what's best for the team and the club."
Odemwingie was full of praise for fellow striker Shane Long who overcame the death 24 hours earlier of his grandmother to score the opening goal and then set up the second-half decider.
He said: "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."