The Czech shot-stopper made the move to the Emirates Stadium in 2015 and during his time in north London the Gunners struggled to mount a Premier League title challenge, with the 2017 FA Cup the only trophy he has added to his CV.
Having won four league titles at Chelsea, Cech says he was surprised at Wenger's desire to focus on playing 'the Arsenal way' - rather than concentrate on getting the results needed to finish top of the standings.
"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 said.
The 36-year-old believes that philosophy of style over substance is beginning to change now Unai Emery is at the helm, but admits it will take some time for Arsenal to rediscover a winning mentality.
"For any club who wins titles in the recent years, you have a team with the know-how how to finish it off - and you can see it in any sport," he said. "I take Tiger Woods - 10 years since he won a major tournament. The longer it goes on, the harder it becomes.
"This club have not won the league for over 10 years so obviously you need to get back into knowing how to do it.
"We started with the new manager from scratch basically and we try to get this mentality of winning every game, progressing every game, working every day and, hopefully, we can build this up and win the title sooner rather than later. That will make the big difference."