The Gunners looked all set to take full advantage of the defeat for leaders Chelsea at north London rivals Tottenham when they headed into the final 10 minutes at the DW Stadium yesterday with a 2-0 cushion following goals from Theo Walcott and Silvestre.
However, Wigan - battling for top-flight survival - pulled one back through Ben Watson before a clanger from goalkeeper Lukasz Fabianski gifted Titus Bramble an equaliser and Charles N'Zogbia wrapped up a famous win for the Latics with a stunning individual effort.
Wenger, for the first time this season, publicly slated his side for a lack of discipline and focus as any slim hopes of hauling themselves back into the titles hunt for a third time were extinguished.
Veteran defender Silvestre - who won four domestic championships and also lifted the European Cup while at Manchester United - agrees the way Arsenal capitulated from such a dominant position is unacceptable, yet maintains the team can produce the "best possible response" by beating Manchester City at Emirates Stadium this weekend.
"We knew that three points was the only result to get back into the [title] race, and 20 minutes from the end, we thought we were going to get that result," Silvestre told Arsenal TV Online.
"Even with the players we were missing, we had enough quality and experience to get the three points.
"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.
"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."
The 32-year-old added: "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."
From being in a position to close within three points of Chelsea, suddenly Arsenal will be looking over their shoulders at Spurs, who following their stunning wins over both the Gunners and leaders with the space of three days are now only seven points behind - and hold a match in hand.
Given Spurs head to Old Trafford on Saturday lunchtime and must also travel to Manchester City, one win out of the final three games - at Blackburn then home to Fulham - should see Arsenal secure at least a third-placed finish.
The fact his side have now failed to win a trophy since the 2005 FA Cup is not lost on Wenger.
However, the French coach as ever remains defiant.
"It doesn't matter if it is difficult or not difficult [to raise ourselves], this job is not only for easy times, it is for difficult times as well, and we have to respond in the next game," he said.
"At our level, you do not want to deal with excuses. You want to show your quality and character in every single game.
"In football, you can always find an excuse for what has happened before.
"I believe what is important is the performance of the day.
"We now have to keep focus and try to win our next game."
Goalkeeper Manuel Almunia was not risked at Wigan because of a wrist injury.
Midfielder Denilson should return to full training this week following a groin problem, while Alex Song's knee injury will be monitored after a scan revealed inflamed cartilage and so the Cameroon international may not be available to face City in Saturday's early evening kick-off.