The Reds fell just short at the end of a magical European adventure as they suffered a 3-1 loss against the three-in-a-row champions.
Van Dijk, who played in six of his side's seven knockout games, believes that those taking joy from Liverpool's setback should actually be feeling jealous.
"Of course we should be proud of ourselves," he told talkSPORT. "All the teams in England want to be in our position right now.
"They act like they're happy, but I think they should be jealous. We were here, unfortunately we lost, but I think we need to take this to next season and make sure we do even better than we did this year."
Following Sadio Mane's goal in the final, Liverpool became the first team to see three players score 10-plus goals in a single Champions League season.