Wenger's side were booed off after a 1-1 draw with Crystal Palace on Sunday left the Gunners fourth in the table, 13 points adrift of leaders Leicester City.
With their title hopes all but over for another season, Arsenal's priority is now Champions League qualification via a top-four finish which they should manage, although failure to beat West Brom could threaten even that limited ambition.
With north London rivals Tottenham Hotspur in second place and still in with a chance of winning the title, Arsenal fans have become increasingly disenchanted with the team and Wenger has called on them to stand behind the players.
"I want our fans to be happy and when they are not, it affects me," Wenger told a news conference on Wednesday. "You do not want to play in a negative environment...
"We are responsible for the performance of the team and it is true that, at the moment, it is not a highlight.
"I hope in the next years, Arsenal will always play in the top three and, hopefully, people won't get disenchanted."
Tickets have been put on general sale for the West Brom match, a rarity for Arsenal home games, and Wenger accepts the fans' patience has been severely tested after his team's a run of only four wins in their last 13 league matches.
"Everybody is free to do what he wants with his season ticket," Wenger said. "We have to live with that.
"It's a Thursday night, it's unusual. We just had a disappointing result at home, maybe that plays a part as well. Is the disillusionment more pronounced? Yeah, maybe."
Arsenal won the FA Cup for the last two seasons but have finished in the Premier League top two just once since their last title success in 2004.
(Reporting by Martyn Herman; Editing by Ken Ferris)
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