Cech has been Unai Emery's preferred No.1 in the league so far this season, despite German international Leno arriving from Bayer Leverkusen for a reported £19.2 million ($25m) fee in June.
Former Czech Republic international Cech has seemingly struggled to adapt to Emery's preferred style of playing out from the back, but produced a string of vital saves in last weekend's 2-0 win over Everton to cement his status as the top choice in the league.
Leno had been restricted to appearances in the Europa League and Carabao Cup, but finally made his Premier League bow in the 45th minute against Watford after Cech pulled up feeling his hamstring following a goal kick.
He went on to keep a clean sheet in a 2-0 win for the Gunners and was satisfied with his league introduction under difficult circumstances.
"It was a difficult start. As a goalkeeper you don't think you will come in and Petr Cech gets injured. I feel sorry for him. I hope it's not too bad," he explained to PLP .
"The two games in the Europa League and Carabao Cup were important for me to get a feel of my defence so it wasn't too difficult for me.
"The big strikers are very good and very strong so we had many problems but our defence did a good job.
"I think we have to improve. We need time but we tried to play football from behind and we have to concentrate as not everything was perfect. It was a good game but not perfect so we have to watch it again and see where we can improve."
Defender Rob Holding was also pleased at getting the better of Watford, and was especially proud of shutting out the Hornets despite fielding two goalkeepers.
"We knew it would be a battle. It always is when you're up against Troy Deeney!" he said.
"We stood up to the battle and though we were tired late on we got those two goals. As long as we matched them physically, we have the players who could get the goals.
"Another clean sheet. It's nice to get that and keep that run going. The manager said he wanted to bring in a winning mentality. We go into each game confident. We're physically fit and we know we can get a result."