Arsenal are only four points behind fourth-placed Manchester City with a game in hand, and if Ozil is back to his best, then the Gunners will no doubt challenge them all the way.
Wenger's side went into the clash at the Emirates Stadium having won just three of their last 10 matches in all competitions, but second-half goals from the Germany global, Theo Walcott and Olivier Giroud got them back on track.
"We know we are going to score goals so if we get that clean sheet we will win games, we needed to go back to basics and we did today, everyone defended well together and we were very well structured".
He said: "When you get a certain amount of points as they did six or seven games ago, you sit and relax and think "we are safe", but actually teams down there go on great runs".
"We started the game good". In matches he has played the French left back has looked more solid defensively than Cresswell, something he will need to show against Arsenal tonight.
Bilic admits West Ham are struggling for confidence right now and says he won't hide away from their struggles.
Player ratingsArsenal: Emiliano Martinez (out of 10) 7, Hector Bellerin 6, Gabriel 7, Shkodran Mustafi 6, Nacho Monreal 7, Granit Xhaka 8, Mohamed Elneny 7, Theo Walcott 7, Mesut Ozil 8, Danny Welbeck 6, Alexis Sanchez 7. "We believe we can win on Saturday".
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But they deserved to win.
"I said to the guys, forget this game". A strong performance here before taking on Swansea would be the ideal boost, and a chance that Slaven Bilic can not afford to pass up if he wants to keep his job.
But Bilic said he has not even contemplated relegation and that he has never once questioned belief in the work he is doing with West Ham. We have players back from injuries.
"So I can take care of myself because I am used to dealing with hard periods but you want people who love the club to be happy, so I'm happy". We are playing a team we have beaten, a team that is five points below us.
Over at West Ham Fan TV however, things were a little more. explicit.
"And then the second half started as the first finished".