The veteran believes his side should have converted a handful of chances at the Vicente Calderon as Atletico Madrid booked its place in the Champions League semifinals.
Koke's goal early in the first half was enough to settle the encounter, though Barca spurned a number of chances during the match, with Lionel Messi guilty of missing two clear opportunities in the first 45 minutes.
Xavi believes Barca would never normally display such a lack of ruthlessness in front of goal and feels his side deserved to at least send the tie into extra time.
"I do not know if Atletico deserved this win," he was quoted as saying by UEFA.com after the match. "We have had several chances to get the draw, we had four or five chances that usually we score. I think we deserved the draw, sending the game into extra time."
Atletico joins Chelsea, Real Madrid and Bayern Munich in Friday's semifinal draw following Bayern's 4-2 aggregate win over Manchester United.