Tuesday's match was a must-win game for the young Reds' hopes of reaching the quarter-finals of the Premier League International Cup.
And Critchley's team responded brilliantly, recovering from last Friday's Premier League 2 defeat to Swansea City by beating the Dutch outfit 3-0.
Rhian Brewster netted a sublime volley to open the scoring and then set up Harry Wilson as the Welshman claimed his 12th goal of the season.
Matty Virtue was also on the mark as Liverpool simply proved too strong for PSV.
“I thought we were fantastic tonight,” Critchley told Liverpoolfc.com. “From the very first minute of the game, with the intensity that we played at, they found very difficult to live with us.
“We got after the ball really aggressively, we played forward and were on the front foot playing in their half of the pitch.
“As bad as we were against Swansea City, we were the complete opposite against PSV, and that’s why when that group of players play like that then they are very hard to handle.”
Reflecting on Brewster’s wonderful volley for the opener, Critchley said: “It was a fantastic goal.
“That’s something we spoke about before the game about not being afraid to go behind the opposition defence, mix our game up and keep them guessing, and we did that well all evening.
“Our second goal was a great counter-attack and then Matty got a great third goal. We had some fantastic moves and I suppose the only disappointment is we’ve not scored more than three goals.
“The players showed a great response and a great strength of character to bounce back. I’m absolutely delighted with the performance and right across the board, the whole team, it was a top, top performance.
“I was actually getting frustrated towards the end of the game because it was ridiculous the amount of chances we created without scoring. I hope we don’t rue those missed opportunities because unfortunately we didn’t get the scoreline we probably deserved.”
Critchley's side will find out in mid-January whether they have done enough to progress in the International Cup as PSV still have to play Newcastle United in the final group game.
Only the six group winners and the two best runners-up will reach the quarter-finals, and Critchley is hoping his side can make it through.
He added: “We want to get through because we want as many games as we can in the second half of the season, we want to be successful, we want to win and we want games that mean something.
“We’ve never qualified out of the group in this competition and we’ve given ourselves a decent opportunity to do that now.”