The Gunners ended a run of four consecutive defeats with victory in Milan on Thursday and continued their recovery with a comfortable win against the lacklustre Hornets in the Premier League.
Speaking to Arsenal Media after the game, Wenger paid tribute to his team for their response to previous results.
"After a difficult Thursday night game, on Sunday morning we still had the spirit to stick together," said Wenger. "For moments we played very well and for moments we had to stick together and suffer.
"Overall, we did very well. I am convinced that is a good basis for the team on the spirit front and overall I am very happy with the spirit of the players.
"The way they responded to a disappointing week, is absolutely remarkable."
Cech became the first goalkeeper to rack up 200 Premier League clean sheets, finally reaching the milestone nearly three months after his 199th.
The Czech keeper has come in for some criticism for recent performances, not least in last week's defeat to Brighton when he was culpable for both goals.
"Petr Cech shows a little bit how quickly things change in football," Wenger said. "He was in hell last week and in heaven today.
"But, I would like to personally congratulate him for a remarkable achievement. I have a huge respect for consistency. It shows a huge level of motivation and intelligence, and he shows plenty of that."
Arsenal now face Milan in the return leg of their Europa League tie at the Emirates on Thursday, where they will defend a 2-0 aggregate lead.