But he recognized the Reds were struggling again from a “good” Seagulls side that created many chances.
He said things could have been worse for his side as they walked away with a 3-3 draw.
Two Van Dijk headers from set pieces gave the Reds their narrow win over Albion at Anfield three years ago.
Since then, the Seagulls have won one and drawn two before the Kop.
They continued that good record under the stewardship of new boss Roberto De Zerbi.
Van Dijk had a torrid period at the back as Liverpool conceded three goals at home in the league for the first time since losing 4-1 to Manchester City in February 2021.
He said: “We were trying to figure out what they were really doing because obviously it was a new manager so we had no idea what to expect.
“But they started quickly and quickly scored two goals.
“In the end we fight back 3-2 and then you have to be careful to get it over the line because they were good today.
“They created chances, made it very difficult for us and we conceded.”
Van Dijk spoke about the problems Albion has caused from Liverpool’s point of view.
He said: “A lot of runners at the back, little pressure on the ball, things we need to do a lot better.
“We say we all do it together, we attack together and obviously we did that very well against Ajax and we did that well in a couple of moments but Brighton are a very good side.
“I think if you look at the results we’ve had against them over the years, a lot of them have been close, it’s always been difficult.
“But today they were definitely in a good moment and made it very difficult for us and it could have been worse.”
Liverpool manager Jurgen Klopp said his side could have won but didn’t deserve it.
He admitted: “I can’t say I was 100% confident that if we were 3-2 up we wouldn’t concede a goal.
“We should defend all three goals better, no question, but in different areas, not just at the last moment.
“The 3: 3 feels like a defeat, although it’s not, and we have to fight our way through it.”
It was almost a dream debut for new Seagulls boss De Zerbi, who said: “I’m really excited for the game. Very proud. We played a very good game. We had the opportunity to score more.”
https://www.theargus.co.uk/sport/23015648.virgil-van-dijks-brighton-verdict-liverpool-thriller/?ref=rss Virgil Van Dijk’s Brighton verdict after Liverpool thriller