Kostas Mitroglou’s hat-trick saw off the Belgian outfit, who slumped to their second defeat in as many Champions League games to stay rooted to the foot of Group C.
But Van den Brom still found time to praise his players' performances despite the result, telling reporters: "It might sound strange after a 3-0 defeat but I am proud of my players, they were brave, confident and attacked from the start.
"I cannot blame any individual, but in the Champions League you get punished for every mistake. Tonight was a classic example of that. However, we must not take the negatives from this, but focus on the positives instead.
"We had to win this match to still be in contention in the group, but we didn't. There are still possibilities for us though. We have to stick with what we saw tonight."
Olympiakos coach Michel was over the moon with his team’s display and, despite Mitroglou’s heroics, he chose to share the acclaim amongst all his players.
"It was [Kostas] Mitroglou's night, but I have to sing the praise of all the players," beamed the Spanish trainer. "Roberto made some fantastic saves and everybody put in a huge effort.
"Even the players introduced from the bench, like David Fuster, responded perfectly to what he was asked to do.
"To win 3-0 away is not a result you expect in this competition. We played well and made the most of our opportunities. [Anderlecht] are a strong team, but we also played very well in every department. We really believed in ourselves and this helped us to win."