Wenger also refused to throw in the towel for the title race despite Arsenal slipping 19 points off the pace, but a top-four place is now the very best they can hope for.
A goalless draw at West Ham made it three games without a win for the misfiring Gunners and further dented their bid to finish in the Champions League places.
Chelsea boss Antonio Conte has already conceded his side, in third, cannot catch leaders Manchester City. But Wenger, whose side lie seventh - below Burnley - said: "I don't want to talk about that.
"It's good for headlines. City are too far away to talk about the title at the moment. We don't give up. Our job is to fight as long as we can and give our best, not to focus on everything else.
"I don't listen much to all that. You want to fight. Our job is to fight, to give everything and see where you finish. City are City. We face the problem with City like everybody else in the league."