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Arnaut Danjuma scored an early goal and Bayern were fortunate they will return to Germany not trailing by more after Villarreal striker Gerard Moreno twice went close.
“It’s a deserved defeat, we were not good,” Nagelsmann told DAZN.
“In the first half we didn’t have enough energy, we didn’t create chances for ourselves and we surrendered control.”
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Moreno hit the post and then curled a long-range effort agonisingly wide after Bayern keeper Manuel Neuer miscued a clearance while well out of his goal.
“We were lucky (not to concede) from that error,” added Nagelsmann.
The defeat ended Bayern’s record run of 22 matches unbeaten away from home in the Champions League.
It was a sequence dating back to September 2017 and a 3-0 loss to Paris Saint-Germain, at the time coached by current Villarreal boss Unai Emery.
“We didn’t manage to put in the performance we wanted,” said Bayern forward Thomas Mueller.
“We accept the 1-0 loss. If things had gone worse, the score could have been greater.
“We saw that Villarreal are not an opponent you can walk all over, despite what certain media were saying. We must prepare ourselves for the second leg and get our revenge.”
Six-time European champions Bayern host Villarreal in Munich on April 12. The winners of the tie will play Liverpool or Benfica in the last four.
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