Newcastle, having lost Anthony Gordon to a red card on halftime, fought back from 2-0 down to level before Rio Ngumoha struck a Liverpool winner ten minutes into injury-time.
Van Dijk said afterwards, "We all know it's a difficult place to come. We know there was a lot of oil on the fire this week to get Newcastle fired up. What happened tonight was expected and, for us, the disappointing part was that we conceded two set pieces. That shouldn't happen but overall great three points, move on and focus on the next one.
"Free-kick, corner kicks the pressure gets on. They had the quality. If you look at the traditional top six here last season there was only a couple that beat them It's always a difficult place to come.
"I enjoy these type of atmospheres, so I was really looking forward to it but we could've made it easier if we don't give them those set pieces, then you give them the boost and the feeling and the drive with the fans behind them but we managed to get the three points and move on."
Gordon was sent off for a challenge on Van Dijk, who also said: "I said to him, if that's not a sending off then I don't understand football. It was strange the referee had to go to the monitor in my opinion. Unfortunately, these things happen in football, if he meant it or not it happened, we move on."
On teenage matchwinner Ngumoha, the Dutchman added: "I'm very pleased for Rio, I've said it to him already it all starts now, he has to keep working hard and stay humble but definitely have to enjoy this because these nights, you can't take them for granted if you're in his position. I'm sure with the players we have he will be back in training and having a hard session tomorrow again."