The result saw the Reds go top of the table, level with Manchester City, though having played a game more.
Van Dijk said, "Obviously we knew their game plan, we knew their quality, especially on the break. But I think on the ball we were just not good enough.
"We lost the ball in difficult situations and if you lose the ball there they can do what they are good at.
"It is frustrating to drop points, but we have to recover and play the remaining games. We have quite exciting games coming up and we must turn this frustration into focus on Villa.
"Give them credit they created good chances as well. We were looking for the equaliser and got it. We were looking for the winner but unfortunately we couldn't get it today.
"We are all human beings so there is a reason why we feel this way when we drop points. But it is what it is and now we have to recover and focus on Villa."