As ever, West Ham went down fighting here in Seville but once again struggled to land a significant blow.
Instead Morocco forward Munir El-Haddadi swept in a superb half-volley from a free-kick on the hour to give the six-time winners the edge ahead of next week's second leg.
And yet again David Moyes was left to rue the inability of his side to take their chances against superior opposition.
But the Hammers' boss has vowed to give West Ham fans something to shout about in the second leg next Thursday night. This tie is still very much alive.
And Moyes urged the London Stadium faithful to match the wall of noise at the Ramon Sanchez Pizjuan Stadium that he believes played a huge part.
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"If we were not creating the chances I'd have been more worried," he said. "My biggest concern was that we wouldn't give West Ham fans a good night at the London Stadium next week. But we will.
"We did a lot of good things, we just couldn't take our chances. Our fans should probably look at theirs for the second leg because they got them over the line.
"We need our crowd to do that and they will do - because we will give them something to shout about next week."
The new West Ham, as Moyes described his side pre-match, acquitted themselves well here in a contest against the Spanish title challengers that many thought would be a mis-match.
Fuelled by belief after their wins earlier this season over Manchester United, City, Chelsea, Liverpool and Spurs, they took the game to Sevilla and at times looked very much their equal.
Once again, however, poor finishing cost them - just as it did at Liverpool last weekend and Southampton in the FA Cup three days earlier.
How Moyes must have wished he had Jarrod Bowen - out injured - when Declan Rice headed across goal for
Nikola Vlasic in the 11th minute.
Somehow the Croatian allowed keeper Yassine Bounou to save when the Hammers should have had a dream start.
Manuel Lanzini could even have drawn them level with 19 minutes left but had his shot blocked when he should have picked his spot.
They'd have profited with Sevilla below par despite their win. Boss Julen Lopetegui bemoaned their inability to score more with 22 attempts on goal.
Their hero, Munir, had only started because of an injury in the warm-up to classy ex-Barcelona midfielder Ivan Rakitic.
Lopetegui said afterwards: "We faced a very powerful team with international players. A team competing for the Champions League next year.
"It's a shame we didn't score the second goal but we were facing the best team in England in terms of strategy."
Rakitic should be back for the second leg. But Declan Rice, immense once again, will be up for the step up in class.
Bowen too will also return for the east Londoners. The climax to this contest will be fascinating.