Nasri produced a tame spot-kick that was easily saved by Sergio Asenjo down to his left four minutes into the second half, after Vitolo had been fouled by Mario.
The on-loan Manchester City playmaker is now without a goal since October.
Sunday's match ended an impressive streak that had seen Sevilla score in 27 consecutive home league matches.
The only other time Sevilla have failed to score under Jorge Sampaoli this season was also against Villarreal in a 0-0 draw at Estadio de la Ceramica in August.
27 - Sevilla had been 27 home league games in a row without failing to score. Asenjo.— OptaJose (@OptaJose) February 5, 2017
Sevilla, who are now winless in two games, stay third after the draw, two points behind Barca and three adrift of leaders Real Madrid, who have two games in hand on their closest challengers.