"You could see that even if the result against City wasn't what we wanted, it had a positive impact on the morale of the team", he said.
The midfielder did not had a great game but after his goal had a purple patch in which he set up captain Theo Walcott for Arsenal's second.
Arsenal dominated the start of the second half and Jose Fonte and Masuaku needed treatment after colliding in the West Ham box.
But Walcott made it 2-0 in the 68th minute, Ozil supplying the cross from the left after a neat one-two with Sanchez.
"There is a relief because we have gone through a bad period".
Arsenal and now in fifth - above Manchester United - and Wenger reserved special praise for Mesut Ozil, who scored once and assisted Theo Walcott's strike.
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.
West Ham are now just five points above the drop zone, and they have lost their last five matches. 'I didn't smell this, I didn't think we would lose five games.
"No one expected Liverpool to draw against Bournemouth, but that is the way it is and that is why we love and enjoy playing in this league".
A timid first-half saw the best chance fall to Welbeck.
Arsene Wenger's guys hold a minumum of one match in hand on all the teams above them and Walcott is hopeful they're back in the Champions League hunt. We have scored over 100 goals this season already so going forward we were always good but defensively we were not good enough. Olivier Giroud came off the bench to score the goal of the night. It is our job to keep the fans behind us because they are also going to be nervous.
Darren Randolph is the current No.1 at West Ham, having displaced his 30-year-old rival in between the sticks earlier in the campaign, but fans are now requesting another change.
Michail Antonio, returning from a hamstring injury, only lasted 45 minutes before being replaced at half-time by Robert Snodgrass. "He didn't feel well", explained Bilic. He was no good after half an hour. "His hammy is really good but around lunchtime, he started to vomit".
Welbeck has not scored a goal at the Emirates Stadium for nearly 12 months and crashed a shot into the side-netting as Bilic threw on fit-again Diafra Sakho in place of Andy Carroll.