Liverpool faced the threat of exclusion from the tournament in the first half, as it was 0-2 behind in front of its host, who beat it in the first 45 minutes with a sweep.
However, the Reds recovered impressively to win 3-2, 5-2 on aggregate and book their place in the Champions League final scheduled for May 28.
Van Dijk said the second-half turn was triggered by Klopp’s half-time talk in the dressing room.
“Klopp told us: ‘Play football, play the Liverpool way’,” the Dutch defender told BT Sport. “He told us to play the way we’ve been playing basically all season.”
He continued: “We demanded to get the ball and move a lot in the opponent’s penalty area and behind his lines, and also show our desire to reach the final.”
Klopp had spoken after the match about returning from a two-goal deficit, but he did not reveal exactly what he had said to his players.
“We knew that in the first half they were a lot better than us man-to-man, but we did not comment on the physical side in the break,” the German coach said.
He continued, “I can’t tell you exactly what I told the players. We talked about how to play football, move around and look for spaces.”