Liverpool were without key players such as Mohammed Salah, Diogo Jota and goalkeeper Alisson for the final and, by the end of a match that went to extra time after a goalless 90 minutes, were fielding a largely second-string team.
"It's emotion, it's everything, I'm so proud of the boys," van Dijk told Sky television on the pitch as the red half of the Wembley fans celebrated.
"All the young boys playing their part in what we achieved today, it's incredible. On to more."
After a lively, end-to-end contest in which both sides enjoyed a string of chances, van Dijk rose to head the winner with two minutes of extra time remaining.
"You should always savour the good moments and this is one of them. You should never take these things for granted," the Netherlands defender said.
