Arsenal have never finished outside top-four under Wenger, who sees increased importance in finishing with one of the four Champions League qualification spots this season.
"It's a good challenge but I think it's certainly possible," Wenger told a news conference. "For 20 years I have done it and it looked nothing. Suddenly now it's important and people realise it is not as easy as it looked.
"We are fighting to have a positive end of season. That’s why you want the fans to stand behind the team."
Wenger said defender Laurent Koscielny, who was substituted at half-time during 2-2 draw with Man City on Sunday, suffered an Achilles injury and is set to have a scan later on Tuesday.
"It (the injury) is serious," said Wenger. "If he has ruptured the fibres then he could be out for a few weeks, if not, he could be available to face Crystal Palace. I will tell you more tomorrow."
Defender Per Mertesacker and midfielders Alex Oxlade-Chamberlain and Aaron Ramsey return from injury layoff and could feature against West Ham.
Arsenal suffered their first home defeat by West Ham in eight years when Slaven Bilic's side won 2-0 at the Emirates last season.
(Reporting by Hardik Vyas in Bengaluru; editing by Mark Heinrich)
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