The 27-year-old has been praised for his dominating displays at the heart of the Reds defence this season, but Liverpool look likely to end the season without a trophy after their disappointing defeat and the Nou Camp.
However, Van Dijk insists Liverpool are refusing to give up on reaching their second consecutive Champions League final.
“We believe. We will keep believing,” Van Dijk said after the loss.
“We know how tough it can be with the quality they have throughout the pitch but we showed at times we could definitely create good chances against them and make it difficult.
“They still have that extra quality but we will try to do everything possible to go through.
“But it is 3-0 and we have a big job to do at Anfield but we have shown throughout the season that we never give up. We need everyone to be together and let’s see how it goes.
“The only thing is that we can only keep believing and keep working hard for each other and stay positive and there is no reason to panic.”
In a further blow to the Netherlands captain, Van Dijk was criticised for his defending by Manchester United legend Rio Ferdinand for his involvement in Luis Suarez’s opening goal on Wednesday.
“Virgil van Dijk here, he’s at fault,” Ferdinand said on BT Sport.
“He can see Suarez there, he’s pointing where he wants it. It’s not rocket science, he’s right in front of him.
“That’s your man, the number nine of the back of the shirt. Static.
“Virgil van Dijk there, static. That’s criminal in that position.
“He’s got to be [Joel] Matip’s eyes and ears. Move Matip where you want him to maybe stop the ball in the first instance.
“But if not you have got to go with your man there.
“He’ll be disappointed with that I’m sure.”
Liverpool welcome Barcelona next Tuesday as they look to pull off one of the greatest comebacks in Champions League history.