It was a welcome boost for the Reds after recent results, but Van Dijk insists they must not take anything for granted after the 2-0 win.
The captain told BBC Sport: "It was a good win and it's good to keep a clean sheet as well – it felt like ages ago. It's a win, we take it and move on.
"It's down to us now to be in the best shape possible to hopefully make it a special evening on Tuesday.
"One game doesn't define – hopefully it does – but it's down to us to keep going. We have been going through a season where we can't build on good performances.
"It's down to us now to prepare for hopefully a special night on Tuesday. That's our main target.
"So, don't get carried away whatsoever. Just look after yourself now, rest up and be ready for an outstanding team on Tuesday that comes here, that plays with confidence and with their fans behind them."
Indeed, looking forward to their Champions League quarterfinal second-leg against PSG, Van Dijk says the occasion demands a full throttle performance. PSG travel to Anfield defending a 2-0 first-leg lead.
He said, "But we are at home and we have to show belief from start to finish that we can do it. It needs a special performance but I've been lucky and privileged that I've been part of special performances.
"So, I believe for sure and I'm going to make sure I bring that across to the team, the boys. But we need everyone to have that same mindset."