Barcelona surrendered a 4-1 first leg advantage to lose 3-0 in Rome and crash out on away goals, but as well as blaming Valverde's tactics, fingers were pointed at an off-colour Messi.
"The final whistle in Rome not only signified Barcelona's Champions League capitulation but also that of Lionel Messi, who lost possession 19 times, shot only two of his five efforts on target, and failed to score throughout the tie.
"From being such an integral part of the win over Chelsea in the last 16, the Argentine arrived at a round in which he has tended to struggle, and that factor became far more than a coincidence as he went missing once again in the quarter-finals.
"There is a clear parallel between Messi's drop-off in the competition and his club's.
With just one title in the last seven years, the Catalans are starved of continental success and the startling way in which their big players go missing on these occasions is really taking its toll."
The Madrid-based paper might have been expected to go in hard on Barcelona's talisman and while another Madrid title, Diario AS, declared him "anonymous", other outlets looked to lay the blame elsewhere.
Catalan daily Sport lamented Barcelona's "Messi-dependancy," while popular nationwide daily El Pais criticised the club's hierarchy for a "path of unlimited spending" and said it was "scary to think about what this club is doing with the best player in history."
One common thread was the effect of Valverde's tactics in what Mundo Deportivo dubbed "a historic debacle". "To be in the semi-finals of the Champions League you need spark and the capacity to take risks," the paper said.
"That is what has defined Barca over the years, but the players and the coach woke up too late."
Ernesto Valverde was criticised for 'conservatism' against Roma Ernesto Valverde was criticised for 'conservatism' against Roma Valverde was also harangued for his failure to react to Roma's dominance after they took an early lead through Edin Dzeko, before Daniele de Rossi's penalty and a late Kostas Manolas header.
"Valverde's conservatism took its toll," said Marca, criticising the coach for not rotating his team in league games despite having the Spanish title practically wrapped up.
"By trying to avoid losing the league when it was already won, he has burnt his players out. The lack of freshness was evident and not just last night, you could see this coming.
"With his team at a clear disadvantage but still in the tie, Valverde didn't go for an attacking solution like putting on Ousmane Dembele when there was still space.
"When the Frenchman finally came on, Roma had their three goals and closed their defence. It was a missed opportunity."