City showed the gap between the two clubs as goals from Raheem Sterling and Bernardo Silva secured a comfortable 2-0 win at the Emirates.
And while fans of any club in the league will understand that keeping City at bay is an almighty struggle, Cech has spoken about how the Gunners will need time to 'adjust' under new manager Unai Emery.
"I think the fans have to understand that when you start building a new team with a new manager and a completely new way it may take time," Cech told the Evening Standard.
"We need to adjust a few things but I think we are on a good way. Yesterday [Sunday] we faced probably the biggest favourite to win the title, next week we have another big game [at Chelsea], but we will be better prepared because we have this game behind us.
"I believe we pushed them more than Chelsea did in the Community Shield. We forced them into a few mistakes with our pressing, we built up from the back and even when we knew the pressure was coming we managed to get out."
Cech came under criticism for his attempts to play the ball out from the back, and was almost at fault for what would have been a spectacularly calamitous own goal as he miss-hit a pass that went just wide of his post.
That moment was jumped on by Bundesliga club Bayer Leverkusen, who sold goalkeeper Bernd Leno, a player renowned for his skill with the ball at his feet, to Arsenal this summer.
Continuing, Cech admitted the team need to improve but is ready to fight for his place in the starting XI.
He added: "We set this out and I think you need to be brave to do that and carry on even when you know the pressure is coming.
"There are things we obviously need to improve, like the second phase to go through that build-up, but overall I think it was a positive performance.
.@Arsenal we share important values which make us a big club not only on the football side . Fair competition, professionalism and sportsmanship are the biggest ones you teach young footballers and it’s sad to see when other clubs don’t share the same values. .@bayer04_en— Petr Cech (@PetrCech) August 13, 2018
"Every player always wants to be in the lineup and it is the same with us goalkeepers," he said. "I will be working hard to retain my spot."