Cech joined the club in the close season following a trophy-laden career at Chelsea, having kept 162 league clean sheets over 11 seasons at Stamford Bridge.
"I have to confess that I started thinking about the record. The most important thing was to win the game and once we got the 2-0 lead and it was going towards the end of the game," Cech told reporters.
"In the last 10 minutes, I was checking the clock.
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"I feel really proud because I believe that this is the best league in the world and one of the most difficult leagues to play for a goalkeeper, and so to have achieved such a record is a great personal achievement," the Czech Republic international added.
"What makes me happy the most, probably, is that these clean sheets have so far brought four Premier League trophies. So, hopefully, we will add clean sheets this season and we will celebrate at the end of the season. This is far more important."
Arsenal host third-from-bottom Newcastle United on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
