The Greek club now stand a decent chance of qualifying for the Round 16 but Silva has refused to set a target for his team who twice went saw leads squandered before delivering a winner in the 66th minute.
"Whichever team comes here to win needs to know how to suffer, to put up with the pressure and I think that was one of the key features here today," he said.
"We can't set limits, we are here and our duty is to improve every day. We know that there are a lot of differences between our team and others like Bayern and Arsenal.
"Our budget is much smaller than theirs but we can't set a limit to what we want to achieve and how hard we work. These kids believed they could take a win in this stadium and worked really hard for it."
Olympiakos now occupy second spot on the Group F table, three points ahead of bottom-placed Arsenal.