Klopp has been in charge at Anfield since 2015 and in 2019-20 led Liverpool to their first league title in 30 years.
"It's a hard one to take, because the manager means so much for us, to me, to the club, to the whole Premier League I think," Van Dijk told Liverpool's website.
"But he made the decision for him and his family. It was always going to be a tough one and it was definitely the case."
Klopp said it would be business as usual at the club, with Liverpool still in the hunt on four fronts, top of the Premier League, into the League Cup final and still involved in the Champions League and FA Cup.
"We have a lot of targets still to achieve this year and why not finish the season on a high and together with celebrations for the boss as well," Van Dijk said.
"Of course this is massive, it's massive news in football... It will maybe even give you an extra boost to do that extra or maybe enjoy it a little bit even more together and make the last part of the season, the last bit of the manager's time at the club, the best time he's ever had."
As captain, Van Dijk will be looking to ensure the squad stay focused on their impressive season.
"For me personally, my mindset is making sure our goals that we have and our targets that we are trying to achieve don't get disrupted by the news," the Dutch defender said.
"That's what the manager wants as well. We want to achieve a lot of things and carry on with the form we have, with the way we are playing, with the players who are doing so well and keeping that confidence."
Liverpool host Norwich City in the FA Cup fourth round on Sunday before welcoming Chelsea on Wednesday in the Premier League, leaving them little time to dwell on the Klopp news.
"We are ready for the FA Cup this weekend and it's going to be a tough one, big one. Let's go out there and enjoy it all.
"Let's make the rest of the season a special one so he can have the farewell that he definitely deserves."
