Jurgen Klopp's men were left on the verge of a Champions League semi-final defeat after suffering a 3-0 loss in the first leg at Camp Nou on Wednesday.
Liverpool have enjoyed a great season, but they are also a point adrift of Manchester City in the Premier League with two games to go as their chances of winning a trophy in 2018-19 slip away.
But star defender Van Dijk said that was not yet a consideration at Liverpool, who make the trip to Newcastle United on Saturday.
"We're not going to think about that," he told DAZN after the loss to Barca.
"We're having a good season and we will try to win something and, if not, we keep working.
"We can be proud of ourselves, we're playing against one of the best teams in the world and obviously in the league we're playing also against one of the best teams in the world.
"We're in both races and I think many, many teams would love to be in our position."
Halfway through the tie.— Liverpool FC (@LFC) May 1, 2019
A big second leg needed at Anfield.
Lionel Messi's brace after Luis Suarez's opener guided Barca to a strong win as Liverpool squandered numerous chances.
However, Van Dijk is retaining belief of an incredible turnaround in the second leg at Anfield on Tuesday.
"Anything is possible in football. We definitely believe. That's how we are," he said.
"We will never give up and we showed today that we can definitely create big chances against them, the only thing is we have to try and score them."
Liverpool will obviously need a strong turnaround to keep their hopes of a Champions League title alive, but they'll also need some help to stay alive in the Premier League.
Following Saturday's match with Newcastle Liverpool close the season against Wolves on May 12, while Manchester City face Leicester City and Brighton in their final two matches of the league campaign.