Petr Cech said Arsenal had to be alert and patient and it paid dividends as they overcame a stubborn Norwich City on Saturday.
Danny Welbeck came off the bench in the second half and lifted Arsenal to a 1-0 Premier League win as the Londoners moved closer to securing Champions League qualification.
Arsenal had been frustrated against an "absolutely brilliant" Norwich team at the Emirates Stadium until substitute Welbeck netted just shy of the hour-mark.
And afterwards, relieved Arsenal goalkeeper Cech said his team-mates deserved to win.
"It was a very difficult game for us because they have been absolutely brilliant for a long period of time," the Czech veteran said.
"They defended very well and very compact. When they had the ball they were dangerous on the counter-attacks.
"We had to be alert and we had to be patient. It took a while to break through and because of our persistence and patience, we managed to get a goal which was vital for us."
Cech, whose Arsenal jumped up to third in the standings as Norwich dropped into the relegation zone, added: "Any game in the Premier League is difficult because every team is well prepared and we needed to be on top to win.
"It was no different today, and as I said they were absolutely brilliant for a long period of time and we are happy we managed to find a way through them and get three points. The way we were patient and searched for the goal, we deserved to win."
Cech also received praise from team-mate Mohamed Elneny after the 33-year-old crucially saved Nathan Redmond's shot with his legs in the first half.
"Everyone knows Petr Cech as one of the best players in the team, where everyone is doing his job and his role is to get the win which was important and may help us fight for second or third place," Elneny said.