Goals from Desire Doue and Khvicha Kvaratskhelia at the Parc des Princes on Wednesday night left Liverpool with a mountain to climb ahead of the return leg at Anfield next week.
Speaking after the match, Van Dijk described the night as "tough work," acknowledging PSG's attacking quality and movement. "We defended with a lot of bodies," he said. "The first goal is a deflection, which is unfortunate.
"We had moments on the break but didn't make the most of them."
Under Arne Slot, Liverpool adjusted their system to deal with PSG's fluid front line, but Van Dijk admitted it required constant communication and risk-taking. "They move everywhere. You have to stay sharp, follow your man and pick the right moments. We had chances to counter but didn't execute well enough."
The Liverpool captain also pointed to key saves from Giorgi Mamardashvili as a potential turning point in the tie, adding: "Hopefully they will be crucial when we look back."
Despite the setback, Van Dijk remained defiant. "We're 2-0 down, so we need something special next week. But we've had big European nights at Anfield before."
Liverpool must first switch focus to a domestic test against Fulham on 11 Aptil at Anfield before hosting PSG, but the message from their captain was clear: "We have to be perfect in everything we do. With our fans behind us, anything is possible."
