Arsenal's breather did not last long, with Sergio Aguero scoring Manchester City's second goal two minutes later.
Arsenal are back in action on Wednesday against West Ham.
Clichy also said that protests aimed at Wenger's removal are part and parcel of the game, even if he does not agree with them.
"Overall I felt it was a mental test and you could see the team was touched on the confidence front", he told his post-match press conference at the Emirates Stadium.
"Both teams want possession and have lots of attacking players, it was a good game for the neutrals".
Man City remains seven points ahead in fourth place, with 10 games to go for Arsenal, including one in hand over Guardiola's side.
Arsene Wenger might think the latest performance should ease the pressure that has firmly camped on his shoulders for the past several weeks, but, in truth, this was another extremely flawed Arsenal show.
Pep Guardiola: 'Winning titles all that matters for Manchester City'
And Guardiola told a news conference: "After the first half when we scored a goal, we forgot a little bit how to play". You are able to think now we are good, now we are able to beat them. "In fact, we conceded goals and that's it".
"In very hard moments in the game - at 1-0 down, 2-1 down just before half-time - our fans could have turned against us".
Going into the match on the back of successive 3-1 defeats the Londoners could have done with a win to keep their hopes of a top four finish alive. While the support, through the game, was outstanding, there were protests outside the Emirates, suggesting the "Wenger out" brigade isn't ready to silently into the night yet.
Within that atmosphere, it's hard for Arsenal or Wenger to contemplate any announcement yet that the embattled manager is extending his 21-year reign.
Manchester City boss Pep Guardiola believes that Chelsea "have the quality to compete" at the top of the Premier League and in Europe next season.
Arsenal had to do without Laurent Koscielny in the second half after the defender suffered an injury to his Achilles and was replaced by Gabriel. "There's time to improve", said Guardiola. I think everyone has to take responsibility.
The Gunners have 51 points and are in sixth place, with two postponed games to go against Southampton and Sunderland. "We play against a team who is stable in what they do".
"I care about Arsenal, about the club, about what we have achieved and what we want to achieve".