"Nothing is good enough anymore. You try to do as well as you can," the Frenchman told reporters on Thursday. "Success is not down to me to judge. Our job is to do as well as we can until the end of the season."
Arsenal are fifth in the Premier League and trail fourth-placed Liverpool, who occupy the final Champions League qualifying spot, by five points but have two games in hand.
Arsenal are also in the FA Cup semi-finals where they play Manchester City next month.
Wenger, 67, admitted Arsenal might find it difficult to secure qualification for the Champions League.
"We want to play in the Champions League next season but we have a tough job because we have six or seven teams fighting for places, and how well we do until the end of the season will depend on that," he added.
A section of Arsenal supporters staged protests calling for Wenger, who is out of contract at the end of the season, to leave prior to home games against Bayern in the Champions League and Lincoln City in the FA Cup last weekend.
Wenger refused to comment on the protests.
"I have nothing to say about that (the protests) anymore. I have talked enough about that," he said.
Injured duo Kieran Gibbs and Alex Oxlade-Chamberlain are doubts for Saturday's match against eighth-placed West Bromwich Albion but midfielder Mohamed Elneny has recovered from an ankle problem in time for the clash at the Hawthorns.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Keith Weir)
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