Goncalo Guedes' strike on the hour secured a 1-0 victory for the hosts at the Estadio do Dragao on Sunday, adding a second piece of major international silverware to go alongside Portugal's Euro 2016 triumph.
Few would have fancied Netherlands – who failed to qualify for that tournament as well as last year's World Cup in Russia – to reach the inaugural Nations League Finals.
Speaking to Sky Sports, Van Dijk added: "Obviously we're disappointed we didn't win the final, but we have to congratulate them [Portugal] as well. We were a bit unlucky today but we have to be very proud of ourselves, keep our heads up, get a well-deserved holiday now and after that make sure we're ready for the qualification.
"At the start of the tournament I don't think anyone would have believed us if we'd said we're going to reach the final. We made a lot of progress, we have to be very proud of ourselves. Now, disappointment is the thing in our heads but we have to keep our heads up.
"It's been a good season, but hopefully next season will be even better. That's what I'm striving for and it's the only thing that you have to do. I'll get a good break and then make sure I'm more than ready for pre-season."
Van Dijk was a key figure in Liverpool's remarkable 2018-19 Premier League campaign, which saw the European champions amass 97 points but still finish second to Manchester City.
"That's what we want to compete again for and obviously [Euro 2020] qualification for the national team is the most important thing for us, we know it, so we'll give everything that we've got and obviously with Liverpool we'll try to compete again with City because they're not going away and neither are we," he said.