After a 2-0 win over Southampton on Monday night at the Hawthorns in which Odemwingie scored both goals, Clarke's side currently sit fifth in the table.
Odemwingie has credited the 49-year-old for improving the current squad, and he feels the ambition in the dressing room is stronger than ever.
"We were saying in the dressing room after the Southampton game that even one point from the previous two games, when we lost so late on, would have put us fourth," Odemwingie told reporters.
"The expectations from our fans are high and after losing against the champions [Manchester City], being so disappointed as a team for us means we are getting better and the ambition is there.
"It is a big plus for us so it's a challenge and the better the results we get, the more confidence grows.
"We are showing a very good quality of football as well so that is where the expectations are coming from because we've been getting results against very good sides.
|100/1||WBA are 100/1 with bet365 to finish in the top four of the Premier League|
"His goal this season was to increase the number of passes we make and that makes you enjoy the game more and brings more excitement. We create so many chances and those things are also very encouraging."
The 31-year-old striker knows the challenge that the Baggies face a challenge to maintain their position but feels it can be achieved if they continue to improve.
"We need to consider also there is a bit of instability amongst the other teams under the top four so that is the hope,” he added.
"The weekend results helped us to bridge the gap that was there and if we keep playing like this, and the rest of the teams outside the top four are still unstable... you never know.
"We will be surprised to finish in the top six or seven but I don't think we will say it is a mistake if we keep playing like we have for the past two months."