A 4-1 victory at Camp Nou had one Barca foot in the last four, but they crumbled in Rome as goals from Edin Dzeko, Daniele De Rossi and Kostas Manolas dumped La Liga's leading side out in the quarter-finals.
And coach Valverde had no excuses for the Blaugrana, acknowledging that they were outplayed by Eusebio Di Francesco's Roma.
"When you lose like this it's always hard," he said. "But it's simple to say that our opponents were very strong from the first minute to the last.
"They applied high pressure throughout and that made it hard to play our game. We couldn't overcome their pressing. They won the second ball, the timing of their goals was important.
"This was a bad day for us. The truth is that they were very good and we weren't.
"It's a painful defeat, no question. We all had the desire to win this but there's only one team left at the end. We've been left behind on the road but there's no other remedy than to continue through what will be a couple of tough days."
Midfielder Sergio Busquets added: "It's very sad to lose after that first-leg lead, but it went badly and they were superior to us all night."