The Reds need to beat Napoli at Anfield on Tuesday to secure a place in the knockout round, and Van Dijk feels the game will test whether or not they are worthy of being in the competition.
"It is our own fault, but we have a way to get out of this," the centre-back told reporters.
"We have not been at our best in the Champions League so we deserve to be in this position.
"If we don’t win we don’t deserve to be in the Champions League. Hopefully that is not going to happen. Hopefully we are going to progress and show that we definitely belong in there.
"At Liverpool there is always a lot of pressure, but it is good pressure. You want to play in these circumstances. You want to be getting the job done before (the last game) but now we are here."
If Liverpool lose to Napoli and Red Star get the better of PSG in Belgrade, last season's runners-up will crash out of Europe completely.
Asked if he felt missing out on the next stage would enhance his side's chances of winning the Premier League, Van Dijk is sure they can keep their maintain their dream of domestic and continental success.
"I won’t answer. Hopefully that isn’t going to happen,” he said.
"I definitely look at the squad and think it can compete on two fronts. We still need to show it.
"We want to compete on the highest level. We are top of the league now, but it could change next week. You never know. The main thing for us is to do everything we can to go through. I am very confident, like always in my team.
"We need to start like we always start at home in the Champions League. We wanted to do that away too but it is not as easy as people might think. We need to start fast, set the tone, put them under pressure and play our game. Be brave, be confident and don’t hide. Show yourself."