The pair were drawn together in the last eight on Friday, while the two teams are also battling Real Madrid for the La Liga title this season.
"I have found memories of Barca but I will fight to beat them, in the league and in a hard eliminator," Villa told AS.
"We must be at our best, but Barca didn't want to see us in the quarter-finals. We're fighting with Real Madrid and Barca for the title, which is already an achievement.
"There is a lot of value in what we are doing, but for now we're not contemplating what it would be like to win the League. One of the mantras of Diego Simeone is game by game and we respect that."
Atletico would move top of La Liga with victory over Real Betis later this afternoon.