Just one point separates the sides in the La Liga title race and they were the first two names out of the hat in the quarter-final draw in Nyon on Friday.
Atletico - three points behind leaders and city rivals Real - hold the advantage domestically and will meet Barca for the first time in European competition, with Valverde confident his side can get the better of the four-time champions.
"We've drawn Barca and will look to get through," he said of Atletico's first quarter-final since 1997.
"We are a team who bases its work on solidarity and persistence and we are uncomfortable rivals for any team."
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