The Gunners overtook Mauricio Pochettino's side into fourth place on Sunday afternoon after Alexis Sanchez scored an injury-time penalty to earn a 1-0 win against a brave and resolute Burnley side at Turf Moor.
The three points saw Spurs climb into fourth, after Spurs were held at the Wembley Stadium against managerless West Brom, as Harry Kane eventually cancelled out Salomon Rondon's opener.
Speaking to the Evening Standard, former Chelsea goalkeeper Cech was asked whether Arsenal could finish above Spurs this season and remained optimistic in his response, stating that it will be close until the end of the season.
“It’s only 13 games in, that’s the most important thing, and there’s so many points to be won. You don’t reach your goals after 13 games, you need to carry on for 38 games and show consistency," Cech said.
“There can be plenty of twists in the table and you see yourselves climb after two wins then have a draw and fall out of the top four pretty quick. It’s packed in there, and I think it will be until the end of the season.”
Spurs finished above Arsenal for the first time in the Premier League table since 1985 last season, as Pochettino guided his side to an impressive second-placed finish while Arsenal failed to make the top four.
Cech has been in excellent form for the Gunners this season, conceding just 17 goals in 15 games and keeping seven clean sheets in all competitions for the north Londoners.
He is almost a certainty to retain his place in between the sticks for Arsene Wenger's side as they go up against Huddersfield at the Emirates Stadium on Wednesday night.