The Netherlands centre-back scored the only goal of the match with a flicked header in the 61st minute to hand the Reds the three points.
"A great win," said Van Dijk to TNT Sports after the match.
"Hard work on a very, very interesting, difficult pitch. [I'm] pleased with the three points. Recover and go again on the weekend."
The result marked only the Black Cats first home defeat of the 2025/26 season, having won seven matches and drawn five games at the Stadium of Light before the loss to the Reds.
"To come here, to play like we did today, [it's] a well-deserved three points. A great game, so we'll take it and move on," added the 34-year-old.
"I think they showed this season how difficult it is to beat them. A lot of credit to them, it's a very hard-working team. With their fans behind them, it makes it a good atmosphere over here.
"I'm proud of the guys. They worked so hard for this today and it's great to see."
Liverpool will turn their attention to Saturday's FA Cup Fourth Round clash against Brighton and Hove Albion at Anfield.
Former Manchester City and Chelsea winger Raheem Sterling has secured a fresh chapter in his career after completing a move to Feyenoord on a deal running until the end of the season.
Liverpool are enduring a difficult Premier League title defence, with scrutiny intensifying over the decision to sell Luis Diaz to Bayern Munich in the off-season.
Arsenal missed an opportunity to re-establish a six-point cushion at the top of the Premier League after being held to a disappointing 1-1 draw away at Brentford.
Ghana star Antoine Semenyo admitted he is enjoying a 'fairytale' start to life at Manchester City after a 3-0 win against Fulham at the Etihad on Wednesday.
