Meanwhile, Valverde also lauded Messi following his Champions League heroics.
With this, he overtook Cristiano Ronaldo in terms of most number of hat-tricks.
Gameday 1 marked the long-awaited return of proper Champions League soccer, and it nearly looked like Messi and Co. never left.
The 21-year-old's driving run earned Messi his free-kick while a sizzling shot brought the goal his bustling display deserved.
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Christian Eriksen's deflected strike gave Spurs a 53rd-minute lead at the San Siro, and the visitors looked comfortable for much of the second half.
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Lionel Messi had said it was time Barcelona won the Champions League again and he played like a man on a mission on Tuesday, scoring a hat-trick in a 4-0 demolition of PSV Eindhoven.
The Camp Nou will be the base of the Blaugrana's success in Europe this season as Ernesto Valverde looks to put a stop to Real Madrid's stranglehold over the Champions League and tonight they were emphatic at the Camp Nou, brushing past PSV with relative comfort.
Then three goals arrived in 15 minutes.
What did you make of Messi's free-kick?
Goalkeeper Milan Borjan made a flurry of telling saves while Napoli's Lorenzo Insigne rattled the crossbar in the first half and Jose Callejon had an effort cleared off the line after the break.
Atletico Madrid got their campaign off to a winning start, beating Monaco 2-1 away from home, while Schalke drew 1-1 at home to Porto. However, Atletico dominated for long spells and struck back before the interval through goals from Diego Costa and Jose Gimenez. He unlocked the Alaves defense to start a 3-0 win in the opening round of the Spanish league. First he whipped in his eighth free-kick of 2018 - right into the top corner beyond Zoet's reach from 20 yards.