Following a scuffed clearance from James Milner, Van Dijk attempted to head the ball back to goalkeeper Alisson but left it short - allowing Ryan Babel to slot it past the Brazil international.
That had cancelled out Sadio Mane's opening goal, but Milner scored an 81st-minute penalty to give Liverpool a 2-1 victory.
It was a rare mistake by Van Dijk, who has played a pivotal part in making the Reds' defence the best in the Premier League this term.
Speaking to Sky Sports , Van Dijk said: "We won the game. Mistakes happen in football and, obviously, a couple of things happen but it is what it is and we go again.
"I'm not giving excuses. I should have handled it better. It is what it is, they scored but we scored again so we won and we have the three points and we go home top of the league and we're happy."
"We knew it was going to be a very tough game, especially second half," Van Dijk continued. "We made it very difficult for ourselves.
"We weren't calm enough on the ball, we didn't create too many options for each other.
"Obviously with my mistake it makes it even more exciting for them. But we have the three points and now we can focus on the national team."
Van Dijk's blushes were partially saved by 72nd-minute substitute Milner, who stopped Liverpool slipping up with his late penalty.
Milner said after the game: "It was me who put him [Van Dijk] in the mire to be fair. The gaffer said to come on and calm it down so the best thing to do is to slice it over the top and put Virgil under pressure.
"But luckily enough we got the result and did what we needed to do.
"What has gone before I feel is probably my fault. The goal is important and I put it away.
"But years of practice goes into penalties and in the game you've just got to go back to what you've been practicing and be calm and know what you're going to do."