Cech was at fault for both goals as he missed a punch to allow Cheikhou Kouyate to head into an empty net before Mauro Zarate beat him at his near post from long-range in the second half.
"It was a collective lapse," Wenger said of Kouyate's opener. "There are many things to say about that.
"I knew that if the delivery was good, we were in trouble before the free-kick was taken. The concentration and organisation was not there from the set-piece -too far from our goal, too much distance to run into, we killed ourselves.
"I haven’t spoken to him [Cech] yet. I can’t see many individual convincing performances today so it’s difficult to single one out.
"Our passing was not incisive enough. Today we have to look at ourselves. We were not good enough."
Arsenal kicked off their 2015-16 campaign as many people's favourites for the title following their capture of Cech from rivals Chelsea - a signing many thought would help bring experience and quality to the Gunners' backline.
Indeed, upon his arrival, Wenger was quoted in July saying: "He has an intimidating presence, that's for sure. He makes the goals look small. That's the kind of charisma he has."
However, Cech - relegated to second choice at Chelsea throughout last season - looked ill-at-ease as West Ham put the hosts to the sword.
Wenger, though, insisted there would be no panic - and again refused to be drawn on reports of an imminent move for Real Madrid frontman Karim Benzema.
"I can only repeat what I’ve said. If an exceptional solution turns up, we will do it. But we must not the mistake of looking outside for solutions because of this result," he added.
"It’s difficult but it’s part of our job. A successful team is down to how you respond to difficult moments. It’s never a clear motorway and we have a difficult start to the season."