Wenger sometimes put 'Arsenal way' of trying to play beautiful football
Wenger departed in May after 22 years in charge having endured a barrage of criticism in the latter part of his reign for a tactical approach that resulted in 14 seasons without a Premier League title.
"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.
"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 (in 2015)."
Spaniard Unai Emery took over as head coach on a three-year contract in May and, after a tricky start, has steered Arsenal to four straight victories as he tries to shape a team that can bring a 14th league title to the club.
Cech, 36, said Emery was bringing back the qualities required to win trophies that had gone missing under Wenger, whose last season in charge resulted in a sixth-place finish, 37 points behind champions Manchester City.
"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," the former Czech international told British media.
"I think the place has become much more demanding in every way so this is great to see because this is what initially drives everybody forward and gives you the kind of kick that: 'I'm not doing enough to start the game' or 'I'm not doing enough to keep my spot in the game,' because the manager asked for precision and hard work every day.
"This is how it should be. We have very healthy competition and we are actually taking the benefit of it."
Cech, who won four league titles in his time at Chelsea, faces competition for his starting spot from the club's new signing, 26-year-old Germany international Bernd Leno.
"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."