The Gunners lost ground in the Barclays Premier League title race with their performance at the Stadium of Light, although Silvestre was not in the team that day.
The veteran was needed off the bench, however, when Arsene Wenger's men bounced back against Standard Liege to seal their place in the knockout stage of Europe's top club competition - the only negative aspect being injuries to William Gallas and Kieran Gibbs.
"I think at Sunderland we lacked a little bit of commitment," he said. "You drop one per cent or two per cent and that's it, you get punished. Against Standard we wanted to rectify this and make sure we got the victory."
Silvestre insists Arsenal put a marker down by getting out of their group with a match to spare.
"It was easy to control the game in the second half as we were 2-0 up. After the disappointment of this weekend it was good preparation for Chelsea too.
"The Sunderland defeat tells us that we can't rest and we have to keep going. We must treat every game the same no matter if it's after an international break or in December when you have a game a week every week. The application has to be the same and so must be the determination."