Bremen were twice forced to come from behind to claim a point, and Di Santo has urged his teammates to push on following such a promising result.
"We might even have won it ourselves and we were a bit unlucky not to," the Argentine, who scored Bremen's second, told the official Bundesliga website. "A point here against a team as good as Leverkusen is great for us, though.
"We're a new team this season with a new mentality compared to last year. We need to focus in the next few matches and look for a win, though, otherwise these draws will count for less."
Bremen return to action next Saturday against Augsburg.