Rafael Benítez and Steven Gerrard both warned against complacency in the second leg but the visitors' performance was so commanding that the normally reserved Liverpool manager claimed there was little room for improvement. "We knew what to do and that was the key for me," said the Spaniard. "We knew they had problems. We had to do the right things and profit from their mistakes. To score three goals and to get a clean sheet is almost perfect."
The only sour note for Benítez was an injury to Fabio Aurelio which looks likely to bring his season to a premature end. There was nobody near the Liverpool left-back when he collapsed to the ground clutching his achilles tendon. He was taken from the field on a stretcher and will have a scan this morning after leaving the ground on crutches. Benítez fears the worst. "It's an achilles tendon injury," said the Liverpool manager. "Normally this injury is really serious."
The Spaniard was more upbeat about his side's display. For all his caution - "we must be careful and approach the second game seriously" - a semi-final against Chelsea or Valencia beckons, evoking memories of their journey to Istanbul and that memorable final against Milan two years ago. "This team is better than the team that won the Champions League," claimed Benítez. "We have got to play one more game and after I hope the semi-final."
Ronald Koeman had declared beforehand that 0-0 "would be a good result" and that lack of ambition was evident throughout. Gerrard, outstanding again, put Liverpool ahead in the 28th minute with a bullet header set up by Steve Finnan and from then on the only challenge the visitors faced was the margin of victory they pursued. John Arne Riise propelled a 35-yard shot into the top corner before Crouch headed in a third, his fourth goal in as many days.
The emphatic scoreline prompted Koeman to concede afterwards that his side, hindered through the loss of several key players, had no chance of overcoming the deficit when they travel to Anfield in a week's time. "It doesn't give us any possibility to go into the next round," admitted the PSV manager. "I think it's not realistic to think we can win [at Liverpool]. If I could make [the players] believe they could still get into the next round I don't belong on this planet."
That might be the case but Liverpool will not treat the second leg as a non-event despite their comprehensive win here. "We are just concentrating on finishing them off," said Gerrard. "We want to be professional in our jobs and worry about the next 90 minutes." The Liverpool captain had provided the impetus for this win, his first-half goal taking his tally in the Champions League to 15, one more than Ian Rush managed in the European Cup.
"I am a bit embarrassed," said Gerrard, who was also making his 50th appearance in the Champions League. "He's someone I watched as a kid and I never dreamt I would break one of his records - I don't think I will be breaking any of his other ones. I am flattered but it's not really important to me. What's important is how well the team is doing. It was a really good performance and hopefully we can go all the way."
Jamie Carragher also reached a new landmark, his 58th appearance in the Champions League surpassing Phil Neal's record. "We broke some records and that's very positive," said Benítez. "We want to see Stevie scoring goals, Carry playing a lot of games and the team winning."
Victory was never in doubt from the moment Gerrard scored, Liverpool taking advantage of PSV's negative tactics to dominate a match that was watched by George Gillett, one half of the club's new American owners. Indeed the victory was so comfortable that Dirk Kuyt, already on a yellow card, needlessly encroached on a free-kick late on to ensure he picked up a booking that means he will be suspended for the return leg at Anfield but available for the semi-finals.
Liverpool could not have imagined a smoother passage into the last four. "We came here not to concede and to get a goal," said Crouch. "To get three is even better. I don't know if it's about rotation but perhaps we are peaking at the right time."