Barcelona superstar Messi won the prestigious honour for a record sixth time on Monday, with organisers France Football declaring his seven-point margin over Van Dijk to be one of the narrowest in the award's 63-year history.
The Barcelona captain finished top of the count with 686 points, just ahead of Van Dijk's 679.
"To be here makes me very proud and makes me want to work even harder and hopefully be here next year again."@VirgilvDijk 💪🔴— Liverpool FC (@LFC) December 2, 2019
While recognising Messi as the greatest player of his generation, Klopp feels Van Dijk should have been rewarded with the prize for his stellar contribution to Liverpool's Champions League win last season.
He told a media conference: "The decisions are made by journalists, right? I see it slightly different. Lionel Messi is probably the best player I have seen in my life, but last season I cannot remember a more impressive season by a defender ever.
"It would have been right if Virgil had won as well. We won the Champions League and he had an outstanding season."
Van Dijk is likely to line up at the heart of Liverpool's defence for the Merseyside derby against Everton at Anfield on Wednesday.
Monday's FA Cup third-round draw conjured up the exact same fixture for the first week of January, with Klopp revealing he would have preferred an easier tie to kick off their cup campaign.
"I didn't run through my living room and celebrate," he said. "It's not exactly what you wish for, but we have no problem playing Everton. It's a big game against big opponents. Obviously, we start the hard way. We cannot change that and we have time to prepare for that Everton game after this one."
Klopp confirmed Liverpool have no new injury concerns for Wednesday's game but says Joel Matip has still not recovered from a knee injury, which has kept him out since the 1-1 draw with Manchester United on October 20.
"Joel needs a bit more time," he explained. "It's healing but not exactly what we wish for."