The side won the 2019-20 Premier League after a 30-year wait for the title but Van Dijk said it there has been "challenging times" for them since then.
"I think trying to stay at the top is the hardest thing to do," he told sports promoter Eddie Hearn's "No Passion, No Point" podcast.
"Everyone wants to see you fall when you reach the top. That is what life is about, especially these days.
"For me I want to give everything I have got until I retire and then have no regrets after.
"I don't want any regrets afterwards, I think that would be the worst feeling you can have. It is going to be challenging times coming up. We are champions -- something that took a while. We should enjoy the moment and go for it."
Van Dijk said it has been difficult for the team to get into the swing of the new Premier League season with no fans present.
"The fans can play a massive part in difficult times during games and also at good times in games," he added.
"When you concede the fans will lift you and when you score they make the opponent go further away from you.
"It's the same case for everyone, but for us in particular everyone knows how difficult it is to play at Anfield with the fans behind us. Hopefully things can change as soon as possible because we need fans.
"It lifts our performances at home but when you play away and the home fans turn against you -- I like that. It gives you that motivation sometimes to do better. It's something I definitely enjoy and that I miss."