The goalkeeper won 15 honours over 11 years at Stamford Bridge, including four Premier League titles, four FA Cups and one Champions League. Two seasons in north London have garnered just one FA Cup.
Cech retains his aim to end Arsenal's Premier League title drought but notes the lack of winning experience in the squad, with Danny Welbeck - previously of Manchester United - the only other with a title winners' medal.
"On arriving at the club, I said to myself, 'Okay, Arsenal have not won the Premier League in 10 years but I want to be the one who helps them win the title'," Cech told French publication So Foot.
"I did not see myself leaving the league which is, in my opinion, the best in the world, and I also wanted to continue fighting for the title. The concern is that we did not have a victor's mentality.
"Chelsea had a simple advantage: on the past ten years, the club has gained more than fifteen titles. The first reason for this, from one year to the next, is that changes in the staff have not been very drastic.
"Come the end of the season, there was always a title, be it the Premier League, an FA Cup, a Champions League or something else. Arsenal have not won anything, beyond the victories in FA Cup, since 2004.
"If you look carefully, there are few who has won the Premier League ... There's Danny Welbeck and me. We have to learn together, we must find this path towards victory.
"My dream today would be to win as much with Arsenal as with Chelsea but I do not think I have ten years left me for that."
