The Gunners host their local rivals in the early kick off on Saturday (18 November) and will go into the game four points and three places behind Spurs. Last season, Mauricio Pochettino's men finished 11 points clear of Arsenal, the first time Spurs had finished above their rivals during Arsene Wenger's tenure at the club, but Cech believes talk of a power shift is premature.
"They've been there in the last few years so now I think they have to make sure they win something to show the progression," he was quoted as saying by the Mirror.
"Success is ultimately winning trophies. We were under pressure the last couple of years, people talking about winning trophies, obviously we are disappointed not to have won the title but we won FA Cups."
While Spurs have already booked a ticket for the round of 16 of the Champions League, Arsenal are sitting out European football's elite competition for the first time under Wenger and are already 12 points adrift of Premier League leaders Manchester City.
More worryingly for the Gunners, they have already lost four times in the league this season, the most of any teams in the top seven, and have conceded 16 goals to Spurs' seven. Cech, however, insisted that while local bragging rights remained important, Arsenal were "not competing" against Tottenham.
"Two years ago when we finished above them we were disappointed because we didn't win the title," he explained.
"There is always one odd year where things can change, but the most important thing for us is competing against the other teams for the Premier League title and for the glory.
"Our target is to win the title and be successful during the season, not necessarily looking at what Tottenham are doing."
Having gone unbeaten in 21 meetings in all competitions against Tottenham between 1999 and 2008, Arsenal have lost twice in their last six games against their local rivals, winning just once in that period.
The last three league meetings at the Emirates have all ended in a 1-1 draw but the former Czech Republic international suggested Arsenal had the players capable of causing trouble to any defence in the league.
Among those, Mesut Ozil and Alexis Sanchez have repeatedly been criticised this season for allegedly showing little interest for the Arsenal cause after they both failed to commit to new deals at the Emirates.
Cech, however, insisted the criticism was not justified and the pair remained committed to the team, even though they could both move to another club at the end of the season.
"With the quality of Alexis and Mesut you are always happy to have players like this in the team," he added.
"But you need them to perform, you need to feel they are committed to the case, I have to say they come every day, they work and as a team we feel that - although there is a lot of speculation, their contracts are different to everyone else's - you can see they are committed to the team."