Eusebio Di Francesco's men suffered a 4-1 loss to the La Liga leaders in the first leg of their quarter-final last week, but Kostas Manolas' dramatic goal eight minutes from time, following an early Edin Dzeko strike and Daniele De Rossi's penalty before the hour, sealed a turnaround for the ages.
"We were the best, much better than Barcelona in my opinion," said Monchi.
"They have Luis Suarez, Lionel Messi, Andres Iniesta, Ivan Rakitic, but the feeling was that we could score.
"Alisson [Roma's goalkeeper] did not make a save, we were better than them in both matches.
"It's Di Francesco's victory, he changed the tactics. It was a hard decision, a risk, but it was the right choice."
Monchi, who oversaw Sevilla's remarkable five triumphs in the UEFA Cup and Europa League during his time at the Ramon Sanchez Pizjuan, hopes the Andalusians can enjoy a similarly historic triumph away to Bayern Munich on Wednesday, where they must overturn a 2-1 deficit.
"I would like to find Sevilla in the semis, but they have to eliminate Bayern Munich," he added. "It's not possible to face a better team than Barcelona."