The Gunners resumed domestic action following the international break looking to carry on from the rout of Manchester United, and they delivered another impressive display when winning 3-0 at Watford in Saturday's late kick-off.
It took an hour, though, for the Hornets' battling resistance to finally be broken when the in-form Alexis Sanchez swept home following a swift counter-attack.
Arsenal put the match beyond the hosts when substitute Olivier Giroud doubled their lead on 68 minutes, and Aaron Ramsey then stabbed in a third.
Arsene Wenger's squad have little time to refocus before they return to Champions League action against the Bundesliga giants, who look in imperious form both in Germany and Europe.
Cech, however, believes the manner in which Arsenal dispatched both United and then Watford under testing circumstances can only stand them in good stead as they aim to kick-start their bid to qualify from Group F following successive defeats.
"It is always difficult going away for the internationals and you come back home and everyone comes back at different times
You have only one day to prepare and you play away from home against a good team that was very solid at home in their previous games," he said.
"We knew it was going to be a difficult game, so we needed to be patient."
Cech added: "We had a really big game against Manchester United last week before the internationals, so when you win those games (you have to) win another game.
"We treat everybody with the same respect, so the three points are vital for us."
Watford manager Quique Sanchez Flores had again set his side up to be hard to break down, a trend which has served them well at home this season since returning to the top flight.
But despite all of their endeavour - with former Tottenham midfielder Etienne Capoue and captain Troy Deeney leading the charge - the Hornets lacked real sting in the final third.
Deeney's raw power caused the Arsenal centre-backs plenty of problems, and the forward believes focusing on the positives of what was a largely industrious display will be key for the challenges ahead.
"It was a harsh lesson in what the Premier League big boys are all about," Deeney said on Hornets PlayerHD.
"We were good for 65 minutes, more than held our own and created a lot of chances, but one counter-attack and that is the difference."
Deeney added: "But let's be realistic, we have just come into the Premier League, we are not expected to just go and beat Arsenal.
"However, we gave the fans something to cheer about and showed what we can do, so the challenge for us now is to make that 65 minutes last 90 minutes against Stoke away (next week)."
Source : PA
Source: PA