The Gunners have won just one trophy - the 2016-17 FA Cup - since the ex-Czech Republic international joined from Chelsea three years ago.
Arsenal have also missed out on a place in the Premier League's top four in successive seasons, finishing a lowly sixth in Wenger's final campaign - their worst finish under the Frenchman.
Cech has seen a change of mentality since Unai Emery took over in the summer, though, with the veteran keeper admitting that Arsenal now know how to win matches by any means necessary.
"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," he is quoted as saying by The Guardian.
"Sometimes you need to make sure you win an ugly game, when you are not playing completely well but you just dig deep, close the back door and win 1-0 no matter how.
"I think this is what we lacked over the last three years, since I arrived. Against Everton, we went through difficult moments in the game but we managed to get the win and with the clean sheet, so this is very positive."