Valverde said that there was an air of disappointment in the Los Che dressing room as they had pushed Les Parisiens hard in the French capital.
"We came here with a hope of qualifying, we knew it would be difficult because they're a good team – but it wasn't possible," Valverde told reporters.
"We hoped to score and complicate things for them, and though we did so in the second half, it was a pity we couldn't keep our lead for longer because we could have caused them more problems. At least we kept the tie alive until the end.
"In the dressing room there is sadness, we are a little sad, but my team has shown its true colours. We leave with our heads held high."
The draw for the last eight will take place in Nyon, Switzerland on March 15.