The Reds, led by centre-back Van Dijk, overturned a 3-0 first-leg deficit with a 4-0 win at Anfield in the return fixture to advance 4-3 on aggregate, reaching the final for the second year running.
Van Dijk is determined that this time, against Premier League rivals Tottenham in Madrid, Liverpool will finish the job, building on the Barca match.
"I could not sleep much [after Barcelona], maybe two hours," the defender told the Guardian. "It was totally crazy.
"From the moment we arrived at the stadium, you had the feeling it could be something special. When Divock Origi scored that early goal, you could feel the belief. Everything was perfect that night.
"It wasn't like we had luck. We totally deserved it because anyone would say a team 3-0 down against Barcelona is not going to do it. Messi's going to score - and if they scored one, it was almost impossible.
"But we did it. It was nuts. You can't really describe it. Hopefully we can finish it off now and make an even bigger memory."
Glory in Europe would provide a fitting end to a season in which Liverpool excelled in the Premier League but fell just short of matching champions Manchester City.
However, Van Dijk insists their ultimate failure to deliver silverware in the league will not impact the side's thinking against Spurs.
"We're not thinking about losing or how we're going to overcome this barrier of losing the Premier League by one point, then losing the Champions League," he said.
"That’s not worth thinking about. I'm thinking about playing to our best ability with all our talent and experience.
"I read that if we win the Champions League, our next two games are the Community Shield and European Super Cup. We can win three cups in three games. It's something we strive for.
"We were close in the Premier League, but now we have a chance to win the Champions League, the big one. We're going to give it everything we've got."