United forward Romelu Lukaku spurned a rare clear opening in the first period when he punted a pass from Alexis Sanchez well over the bar and the Belgian had a goal ruled out for handball late in the second.
Sevilla fired 25 shots at De Gea's goal while United only had six attempts, only one of which was on target. United coach Jose Mourinho, however, said he did not feel his side had been fortunate to leave Spain with the tie still wide open.
"No, I'm not relieved. I think we finished the game with more space than we had in the beginning, with more chances of scoring the goal," he told a news conference.
"The stats are what they are. Sometimes you have 15 shots, but 13 of them were what I call statistic shots. So I really feel the result reflects what the game was like. If you ask me is it a good result, I say it is not good, it is not bad."
The second leg takes place at Old Trafford on March 13, where United will be looking to reach the last eight of the competition for the first time since 2014, with Sevilla hoping finally to get past the last-16 barrier they have failed to overcome in three previous attempts.
Pogba did not manage to answer his many recent critics, who have questioned his influence over the last two months. He was unable to engineer many attacks and sent a long, hopeful shot well wide of goal in the second half.
United's latest high-profile signing, Alexis Sanchez, also had a night to forget in his first European game for the club since joining from Arsenal in January as he saw little of the ball and was hauled off for Marcus Rashford in the 75th minute.
Muriel paid tribute to De Gea for denying him and said he was disappointed his side did not take their chances.
"He moved his body well, I could have hit it in the corner but I went for power over placement and he's a great goalkeeper," Muriel said.
"When you play matches like this the key is scoring in these little chances like that, but in general the team played very well. We played exactly as you should: we were disciplined in every stage of the game but we leave here feeling a little bitter that we couldn't score."
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