Against Everton, coach Unai Emery chose to bench French youngster Matteo Guendouzi, who has performed well so far this season, and handed Uruguayan Lucas Torreira, another summer arrival, his first starting for Arsenal in the English Premier League.
"What we lacked in the past - I would say the "Arsenal way" was more important than getting the points sometimes and this is not how you win the league", Cech was quoted by The Independent as telling reporters after Sunday's 2-0 home win over Everton.
Wenger ended his 22-year tenure with a disappointing sixth-placed finish last season and Cech feels there is an added impetus on addressing recent shortcomings now Unai Emery has taken charge.
"I take Tiger Woods - 10 years since he won a Major tournament (in golf) and the longer it goes, the harder it becomes".
Arsenal lost Greek defender Sokratis to injury, leaving the Gunners even more vulnerable to Richarlison, who immediately seized on Sigurdsson's pass and unleashed a powerful drive that forced Cech to save.
"Then we scored the goal and I chose to stop it and think again about who we need next".
Reflecting on the early struggles in a response to a question from the Gazette Cech responded saying: "It's been a new way for the whole team and we need to find a way to use it to our advantage but every day and every game we are improving".
Silva: Poor decision cost us
Some Arsenal fans have slammed Aaron Ramsey on social media despite the midfielder supplying two assists during the win over Everton on Sunday afternoon.
Cech won four league titles at Chelsea before moving across to London in 2015 to join Arsenal, who have not lifted the trophy since 2005. "That will make the big difference".
While he said that Torreira made a good performance for Arsenal, he also admitted that Guendouzi, too, was performing well for the North Londoners.
"But we managed to deal with it and got our first clean sheet of the season which is big".
The Gunners' next league game comes up on Saturday, 29 September, against Watford.
"It's a bit odd for me that the assistant could not see where Aubameyang was but we can all make mistakes".More news: OPEC raises forecast based on USA oil production