They had chances and were the better side for large spells of their 2-1 defeat at the Ramon Sanchez Pizjuan Stadium, but Bayern, like Barcelona, needed only a moment to strike.
Vincenzo Montella said afterwards his players had not had luck on their side and there was some truth in that.
Franck Ribery's cross was heading wide until Jesus Navas dangled out a foot and Thiago Alcantara's header would probably have been saved had it not been diverted by Sergio Escudero.
But for all their energy, verve and aggression, Sevilla have shown this week they still lack the control to manage matches against elite opposition.
Against Bayern, they led for only six minutes, allowing their opponents to reach half-time level when they could easily have been two goals down as Pablo Sarabia, Sevilla's scorer, had planted an earlier, easier chance wide.
“With that opportunity it was a pity,” Sarabia said. “I tried to adjust it to the maximum and I did not hit the target.”
Against Barcelona they had conceded twice after holding a deserved 2-0 lead with just two minutes to go.
“We were a little lacking this side of experience… how to talk to the referee, and to be focused on small details,” Sevilla striker Wissam Ben Yedder said.
“We know that it will be very complicated because now we have to (score) two goals there but we know that everything is possible.”
Bayern coach Jupp Heynckes said he believed the timing of his side's equaliser, just before the break, was a psychological turning-point.
Scoring twice at the Allianz Arena next week is not beyond Sevilla, who can take heart from the numerous occasions they broke through Bayern on Tuesday — but it is hard to see them keeping a clean sheet.
After the second leg, they play Celta Vigo and Villarreal in La Liga before a reunion in the Spanish Cup final with Barcelona, who this time are likely to have Lionel Messi for 90 minutes.
If they are knocked out by Bayern and lose to Barca, Sevilla will be relying on their league position to qualify for Europe next season — they currently sit seventh, only two points ahead of Girona.
Bayern, meanwhile, know they will have to improve with striker Robert Lewandowski, whose name continues to be linked with Real Madrid, virtually anonymous.
It was the 34-year-old Ribery who made the difference. “In the first half we were not well organised,” Ribery said.
“We did not play in front, at the break the coach gave us a telling off. Seville is a very good team who plays very well in football, but we reacted well after the 1-0.
“We must not believe that we are already in the semi-finals.”