Ancelotti's men led early but were reeled in by the persistent hosts, with two Carlos Bacca goals helping Sevilla move closer to fourth-placed Athletic Bilbao, and within six points of a UEFA Champions League spot.
The Italian tactician said Sevilla's exploitation of Real's defensive frailties meant his side were not deserving of the three points.
"I don't think we deserved to lose," Ancelotti said.
"On the one hand we could have because we didn't prepare well for Sevilla's counter-attacks and that is how they scored both goals.
"We took the lead and could have scored more goals. Then they scored two goals in the same way when we needed more balance."
Ancelotti refused to single out Xabi Alonso for criticism, after the defensive midfielder gave up possession in the lead-up to both of Sevilla's goals.
"Alonso is not at fault, he miscontrolled the ball, but we have to cover his back and we didn't," he said.
"That is where both goals came from.
"Cristiano Ronaldo was annoyed because we were losing the match, nothing more.
"Now, La Liga is more complicated because we are behind (Atletico and Barcelona). It's more complicated but not impossible."
Ancelotti also refuted suggestions Real struggle in big matches, having lost two on the spin against Barcelona and now Champions League-chasing Sevilla.
"It's not a problem. The team has lost against smaller teams," he said.
"La Liga is complicated and it has strong teams and every match is difficult. We have to think about ourselves.
"We lost two matches but we have to believe we can win it. We are behind but we have to believe it is possible."
Real defender Marcelo said he was sorry for the capital club's performance, which has seen them lose their advantage in the La Liga title race.
Atletico Madrid claimed outright lead in Spain's top flight following Wednesday's games on 73 points, one ahead of second-placed Barcelona, while Real (70 points) dropped to third.
"We knew the end of the season was going to be tough. Every game is like a final. We have to fight and keep fighting and apologise to the fans of Real Madrid," the Brazilian said.
