A dreadful run of four defeats in six Premier League games has seen them slip off the pace in the race for the Champions League places and seen the pressure increase on Wenger with many supporters protesting against him in recent weeks.
But a better performance - and result - against Manchester City at the weekend has Wenger feeling more positive about his team's prospects for the remainder of the season.
And writing ahead of the match with West Ham, Wenger has moved to put his side's woes in some perspective.
"Finishing in the top four is a good challenge but I think it is perfectly possible," he wrote in the matchday programme.
"The experience of having done it before will play a part of course, but I think it is just about sticking together and continuing to right. If we show the same spirit we showed against City, we will win football games.
"We were unbeaten for 19 games this season, and I think it's a good opportunity to remind people we are not fighting to not be relegated, we are fighting to have a positive end to the season.
"That's why you want the fans to stand behind the team and that the debate at the moment is about that."