Spurs finished ahead of Arsenal in the Premier League for the first time during Arsene Wenger's tenure last season and could open up a seven-point gap over the Gunners with victory at the Emirates Stadium this weekend.
But Cech, asked whether the balance between the rivals had changed, said: "No, I don't think so".
"It does hurt as it's been a long time since that happened".
Manchester United legend Ryan Giggs has claimed that Tottenham have the ability to get the "upper hand" over Arsenal for years to come if they start to consistently get results against them.
"They have got a really good squad, an excellent manager in Pochettino and they are great to watch".
Spurs were 3-1 winners against Champions League holders Real Madrid at Wembley last month after already beating Borussia Dortmund at the home of English football.
Most of Mauricio Pochettino's star players will have had breaks from football during the worldwide fixtures, with the likes of Harry Kane, Dele Alli, Jan Vertonghen and Hugo Lloris all picking up injuries that kept them out of contention for their countries.
Cech, whose team take on Spurs in a derby on Saturday, told Sky Sports Spurs needed a trophy in order to show "progression".
"Form often goes out of the window with derbies but Arsenal have tended to dominate, so Tottenham are naturally relishing getting some revenge".
Giggs still believes that the EPL title will be between the two Manchester sides in this campaign, but he thinks Tottenham won't be far behind.
Parlour is a big fan of how they do things too, having previously praised Harry Kane, he is also a fan of Tottenham's style of play and ability to beat a high calibre of teams.
So if the Gunners don't beat Tottenham this weekend, will that confirm that Giggsy is right, and Spurs have resigned St. Totteringham's Day to the bin for the forseeable future?
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