The Premier League champions began strongly at Emirates Stadium on Wednesday night and deservedly took the lead 20 minutes in when Sadio Mane rounded off a slick team move.
However, the hosts scored twice against the run of play before half-time following rare errors from Van Dijk and Alisson Becker.
The Reds were the game’s dominant force throughout - registering 24 shots to the hosts’ three and having nearly 70 per cent possession - but were unable to convert their pressure into further goals.
Van Dijk told Sky Sports: “Well, obviously the goals we gave them as a present.
“I think until their first goal it was totally us, we dominated, put pressure on them and we gave them two goals and obviously then it’s difficult to come back.
“We created some opportunities, I think they tried to break on us at times but obviously if you give the goals away like this, like we did today, including myself, then you get what you deserve.”
The Dutchman went on to dismiss the idea that such mistakes can become more common in a team after they have mathematically secured the title.
“It’s too easy to say that, it’s too easy to blame that as well I think,” he said.
“If you watched the game then you can see that until I made a mistake, there was nothing wrong. We played well, I had a feeling we could win here comfortably at one point, but obviously if you give them the goals you see what happens.
“Unfortunately I made the mistake, I take the blame for it of course. I take it as a man and we move on.
“We’ll try to win the last two games and get a well-deserved break, but we don’t need to forget that we had a fantastic season already.”
It was announced earlier on Wednesday that Van Dijk and his teammates will lift the Premier League trophy in a special ceremony on the Kop following next week’s meeting with Chelsea.
The No.4 continued: “It will be a dream come true. Being champions of the Premier League is already a dream come true.
“Obviously tonight the disappointment is what’s in my head at the moment, but I go home and it will be all fine. That’s the life of a football player: sometimes you win and you be the hero, and sometimes you can be the villain in certain cases.
“Today, like I said, I made a mistake - I take full responsibility for that and we move on.”