Simons was dismissed in the first half of Tottenham's clash with Arne Slot's side after a VAR review showed the 22-year-old had raked his studs down the back of Van Dijk's calf. His dismissal opened the door for Liverpool to secure a win that moves them up to fifth in the Premier League table, while Spurs dropped to 13th.
"I don't think there was any intention to hurt me but obviously he hurt me and then the referee and the VAR made the decision to send him off," Van Dijk said. "I spoke to him. It's a chat that no-one needs to know."
Liverpool's victory came at a price, with forward Alexander Isak being forced off the pitch just moments after scoring the visitors' opening goal in north London. The 26-year-old looked in a great deal of pain following a coming together with Spurs defender Micky van de Ven, and the Reds now face an anxious wait to discover the extent of his injury.
"Injuries unfortunately are part of football and hopefully with Alex it's not too bad," Van Dijk said. "He scored a great goal. It's too soon after the game to know [the extent of it]. He will need to be assessed.
"We all saw how bad it looked with Alex but hopefully it won't be too bad."
Liverpool are now unbeaten in six games in all competitions but came close to conceding a last-minute equaliser against nine-men Spurs, who finished the game strongly.
Reflecting on the performance, Van Dijk said: "The immediate reaction coming off was that it was a chaotic last five to 10 minutes. It wasn't great but to get the three points is massive. There was nothing wrong up to us conceding a goal. We need to analyse the last part but personally I'm very pleased and it's on to the next one.
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"When you concede a goal and their fans get behind them like they did, it's never easy to make the right decisions and find the right solutions. That's something we can improve but I don't think it's worrying. It's a transition and we need to keep getting better."
The Dutchman added: "Winning more, getting results, is always positive. Losing games, especially at a club like Liverpool, is always bad. For us it's about staying calm. Taking each game as it comes.
"Today we won. Now we have a couple of days off. We will recover and then we will focus on Wolves. It will be a tough game. I saw their game against Spurs. Wolves will make it difficult for us and we have to be ready for that.
"First we have Christmas. Being with your family and being healthy are the most important things in life."
