The Frenchman confessed that his side rode their luck to overcome a plucky comeback effort from Crystal Palace.
The Gunners looked to be home safe after taking a 2-0 lead in the encounter, but Alan Pardew’s men rallied in the dying moments to pull a goal back through Glenn Murray.
The spoils could well have been shared as Palace struck the post in the last minute of injury time, but Arsene Wenger’s men hung on to claim a valuable three points in their search for a top-four finish.
The French manager admitted that his side rode their luck at the end of the game and were guilty of switching off.
“Certainly they thought that it was done,” Wenger said when asked about his players, reported in The Daily Mail.
“We know in the Premier League that it's never done, especially at 2-0. With that ball on the post we were a bit fortunate.
“We can learn from every game. I believe that the players know that maybe they switched off a little bit too early.
“Overall I still must say that our central defenders played very well today against a very direct and a very physical game at the back.
“We missed goal number three and when they came back to 2-1 we were a bit lucky, a bit fortunate. We did well so overall I'm pleased to have won three points in a place like this. I feel quite strong and let's just continue to fight and be tight until the end.”
Arsenal now host Monaco on Wednesday night in the Champions League and will hope to record a positive result to make their subsequent trip to southern France more comfortable in a fortnight’s time.
Southampton can demote the Gunners to fourth place on the domestic standings if they beat Liverpool at St Mary’s today.