The Blaugrana produced a bright display at the Ramon Sanchez Pizjuan Stadium but could only come away with a point in a 1-1 draw.
Alejandro Gomez prodded home the opener for the hosts from a smartly taken corner before Ronald Araujo equalised for the visitors with a fine header on the stroke of halftime.
Sevilla were reduced to ten men in the second period after Jules Kounde was dismissed for hurling the ball in Jordi Alba's face but the closest Barcelona came to a winner was when Ousmane Dembele struck the post with a curler late on.
The point leaves Barcelona in seventh position, two points adrift of the Champions League places.
Nonetheless, Xavi was satisfied with his side's display but felt they deserved to come away with maximum points.
"We have lost two points; we deserved to win, even when it was 11 against 11," he told Movistar.
"It will be difficult for me to sleep because we should have won. Sevilla were able to cool the game down; they are a veteran team, they know what they are doing and they work very well tactically.
"This Barca is close to the one we want, to be protagonists and be brave. It is the right way.
"I have seen a Barca with personality. It is what we want and the team is growing.
"We were good at high pressuring, recovering after losing the ball and the circulation of the ball. We competed very well, despite the draw."
Barcelona's next game will be away at Real Mallorca on January 2.
