Cech's arrival after an 11-year trophy-laden spell at Chelsea was met with great optimism by supporters and hailed as the missing piece in Arsenal's quest for a first Premier League title since 2004.
But the Czech international was far from his commanding best at the Emirates, failing to deal with Dimitri Payet's free kick in the build-up to Cheikhou Kouyate's header before being beaten at his near post by Mauro Zarate's low strike.
"I haven't spoken to him (Cech) yet," Wenger told reporters. "I can't see many individual convincing performances today so it's difficult to single someone out.
"It was a collective one. I think there are many things to say about that. I knew that if the delivery was good, we would be in trouble before the free kick was taken.
"We have enough experience at the back. If you look at our back line, I think the youngest age is 30."
The Gunners were hoping to make a flying start and show that they are serious contenders to challenge for Chelsea crown.
Against Slaven Bilic's well-organised West Ham, however, Arsenal struggled to impose themselves and Wenger was frustrated with the way his team went about their business.
"I think our performance was not convincing," the Frenchman said. "I felt we were a bit nervous and we rushed our game a bit.
"We didn't always respect the basics. We wanted to be too quick going forward in first half.
"I don't think we were too confident, I would rather say too nervous maybe.
"On top of that, I feel we gave two very cheap goals away and they were at the wrong moments - just before and after halftime.
"We gave ourselves a mountain to climb."
