Liverpool fought through two hours against Chelsea at Wembley, going to another penalty shootout and winning 6-5 to clinch the FA Cup.
The victory took its toll, though, with all three of Van Dijk, Mohamed Salah and Andy Robertson forced off with fitness concerns.
Salahs appeared to be the most troubling, with the Egyptian withdrawn midway through the first half with a groin problem, but Robertson is likely to escape a layoff after a suspected cramp.
Van Dijk, meanwhile, should also avoid the treatment table, with Klopp providing a brief update in his post-match interview with BBC Sport.
Virgil is fine, I think, he explained, but a little bit tired in the muscles.
It is likely that the Dutchman will sit out for the trip to former club Southampton on Tuesday night, however, with a focus on the Premier League closer at home to Wolves and then the Champions League final.
Joel Matip replaced Van Dijk at Wembley and should start at St Marys in midweek, while there is a chance Joe Gomez is handed a rare start at centre-back, too.
Meanwhile, Kostas Tsimikas could follow up his FA Cup-winning spot-kick with another start in the league, with it unlikely that Robertson is risked either.
There will almost certainly be a wait to determine the extent of Salahs injury, with a scan expected upon the return to Merseyside this weekend.