Mauricio Pochettino's side finished above Arsenal for the first time since 1985, finishing second behind Chelsea while Arsene Wenger's men were way down in fifth place.
Spurs face Arsenal at the Emirates Stadium in Saturday's lunchtime kick-off, the first time the two sides meet this season as Pochettino looks for his side to secure a sixth Premier League win in their last seven top-tier outings.
However, former Chelsea goalkeeper Cech claimed that Spurs are no better than Arsenal, and described Tottenham's superior second-placed finish as "one odd year", as well as stating Pochettino's appointment has paid dividends.
"I don't think there is a power shift," Cech said. "One odd year where things can change, the most important thing for us is that we are competing against Premier League sides for the title and the glory, not just Tottenham Hotspur.
"Three years ago, when we finished above them, we were disappointed because we didn't win the title. The big factor was the appointment of Mauricio Pochettino. His work at Southampton showed he is a very capable manager. They have young, talented players - well balanced.
"Last year was a strange season, we had more points but we finished outside of the top four. This season we need to get a Champions League spot."
Tottenham are on a good run of form against Arsenal, losing just once in their last seven league and cup outings against the Gunners.
Pochettino will be looking for his side to continue that run of form with three points away from home, which could see Spurs move into second place above Manchester United if Jose Mourinho's side fail to beat Newcastle United at Old Trafford.