De Rossi's second-half penalty and Kostas' late header sealed Roma's passage to the last four as the La Liga leaders left the competition at the quarterfinal stage for their third time in a row.
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. "This is the toughest blow I've received in the whole time I've been at Barca because of how it happened".
"I would be lying if I told you we can take something positive from this", midfielder Sergio Busquets told beIN SPORTS.
Barcelona was eliminated by eventual runner-up Juventus last season, losing 3-0 in Turin and being held to a scoreless draw at home in the second leg.
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"We want to be contending for the Champions League title year after year", Barcelona president Josep Bartomeu said. "It is a massive disappointment given the season we had been having". We have to try and win them because we have not won anything yet.
Marca, on the other hand, gave a more positive verdict: "He was the only one who demanded the ball and tried to save the team". "I thought that when the game was equal, with them needing one more goal, there was enough experience in the team to see the game out", he said.
"For a spell, he was advising the president and right now, when there's a loss of character at Football Club Barcelona that can somehow staunch the flow last night or in Paris past year at 4-0 or against Chelsea - Chelsea came very close at the Camp Nou to doing what Roma did last night in the Italian capital".
This was Barcelona's first Champions League loss under coach Ernesto Valverde, who replaced Luis Enrique at the end of last season. The truth is that they were very good and we weren't.
They are unbeaten in La Liga and had only previously lost once all season, to Espanyol in the Copa del Rey.