Messi moved ahead of his great rival Cristiano Ronaldo’s tally of trebles in the competition after paving the way for a 4-0 win with a stunning 32nd-minute free-kick.
The Argentinian scored twice more after Ousmane Dembele had got his name on the scoresheet with a brilliant solo strike, prompting Valverde to sing Messi’s praises in the post-match press conference.
Valverde said: “He does extraordinary things and makes them seem routine.
“Today it was three goals, and he unlocked the match with his free-kick. The strike was masterful and he simply doesn’t tire of scoring hat-tricks.”
Valverde was pleased with the way his players responded after their gruelling weekend win over Real Sociedad, but he acknowledged it was far from easy until Messi broke the deadlock.
“I’m satisfied with the 4-0, it’s a normal result (when you look at how the match progressed),” added Valverde.
“They played well on the counter-attack and we knew it would be difficult to get the first goal.
“After the second goal we were calmer and found things easier, it’s always difficult to open teams up at first.”
PSV coach Mark van Bommel insisted the final scoreline flattered the hosts, and claimed his opposite number Valverde had agreed with him.
Van Bommel, who questioned the awarding of the free-kick from which Messi opened the scoring, said: “He found 4-0 too much, and I agreed with him.
“Today I have seen that we are well on the way, but that we cannot always determine what is going to happen.”
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