Head coach Antonio Hidalgo admitted his players struggled to cope with a physically demanding week, having gone into the game short of both rest and options.
"We were uncomfortable, any mistake against us gets punished, and we had issues with recovery and players who were really stretched," he said.
Hidalgo had started Yeremay and Angeliño down the left flank, but neither had a strong game, and both were inconsistent throughout their time on the pitch.
"Sevilla are a solid, well-drilled team. We had players who arrived just about ready after some of them didn't complete pre-season," he added.
Sevilla boss Luis García Plaza felt his side deserved more than a narrow win, having dominated large spells of the contest.
"We were very deserving of the victory. In the first half I think we were already superior, but we weren't quite taking advantage of our chances. We had a huge number more shots than them," he told DAZN. "The team did a spectacular defensive job, but without dropping back — only when it was necessary — keeping our identity and spending a lot of time in their half. We're in a good moment and, with all due respect, I think we fell short."
García Plaza credited his side's adaptability for nullifying a Deportivo team that shifted shape repeatedly through the game.
"Hidalgo has a lot of variations throughout the match: he started with a back three and I switched to a back four, then the forwards tucked in more centrally... we had to be very alert and adapt," he said, adding that Sevilla's travelling support — around 1,000 fans on a Wednesday night — had also lifted the team.
With 13 points from a possible 18, García Plaza urged caution despite the strong start.
"We have to be humble, just as we try not to make a drama when things go badly, we shouldn't get carried away when things go well. It's a dream start, but the competition is very tough," he said, before looking ahead to a daunting trip to face Barcelona. "They're frightening, but we're going to compete with them. It won't be easy, but we're in a good moment."
For Deportivo La Coruna, the defeat ends their unbeaten start to the campaign, but Hidalgo's players have little time to dwell on it, with the visit of Real Betis already occupying their thoughts.