Klopp, 56, announced on Friday that he would be standing down as Liverpool boss at the end of the season.
The bombshell news sparked reaction all over the world of football, with warm tributes being paid to Klopp in the aftermath.
Van Dijk admits the news was hard to swallow when he heard it alongside the other Reds players but focus now turns to ensuring Liverpool have the most successful conclusion to the season possible.
“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?
“For us and for me personally as well, I want to make sure the rest of the boys think like that too.
“We all want to achieve so much and that mindset was already there since pre-season and that doesn't change.”
Liverpool are fighting on four fronts with the club top of the Premier League, into the Carabao Cup final and competing in the Europa League and FA Cup as well.
Van Dijk believes Klopp’s impending exit could even provide his side an extra incentive to make the rest of the season an occasion to savour.
“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.
“You want to be there and you want to be there for the team, be there for the manager. Let's make the rest of the season a special one so he can have the farewell that he definitely deserves.”