The Gunners conceded three goals in the last 10 minutes as their Premier League title hopes went from slim to none at the DW Stadium.
Silvestre admits he and his team-mates thought they had the match won after going 2-0 up just after half-time, and has called on them to make amends in their last three games of the season.
“We will analyse what happened, but energy-wise we can give a lot more in the last 20 minutes. Instead of a response, we just let them do it,” said the Frenchman.
“I do not understand why we did not control the game in a better way. Normally we can play our football and develop attacks, but after we went 2-0 up, we stopped playing and working hard. You cannot rest on what you have been doing in the past. Every time you have to prove yourself and that you are the best team.
“We have to respect the club and the fans who travelled to Wigan and show them we can respond in the best way possible, which is a win against Manchester City.
“We need to get back to winning ways, back to happy days, but it won’t come performing like that. We have to work harder.”
With in-form City visiting the Emirates Stadium on Saturday, Arsenal manager Arsene Wenger is anxious to restore belief to his flagging troops, who have lost three in a row, and is not in forgiving mood.
“This job is not only for easy times, it is for difficult times as well, and we have to respond in the next game,” said Wenger.
“At our level, you do not want to deal with excuses. You want to show your quality and character in every single game.”