Liverpool were beaten 3-2, with Van Dijk conceding a penalty converted by Igor Thiago on the night.
The Dutchman said afterwards: "Disappointed. Disappointed for losing here. We know obviously what their strengths were and what they obviously look to try to do. The first goal is something obviously we knew, so we have to be spot on in that - it's a quality of them.
"Then the second goal to concede is obviously not great. Then the penalty. It was just a very disappointing night overall for us. It's tough to take but it's the reality and we have to keep going."
On the penalty, Van Dijk said: "I don't know. The referee said the ball was on the line, but then he put the spot first two metres outside the box. So, I didn't know what really was going on. In the end, he gives it. That's obviously not great."
He continued: "It's the reality that we lost today, and that's the only thing. We have the next game on Wednesday against an opponent that made already our life difficult this season. We have to turn our mindset pretty quickly in order to be ready for that, because they'll come to Anfield to try to hurt us even more.
"Obviously this is a tough one to take, we can't deny that. It's been not an easy moment. We were trying to build on the performance that we had in Frankfurt but unfortunately this was not a nice evening to have."