Despite Cristiano Ronaldo going off injured early on, Real went ahead through Sergio Ramos, but a late header from substitute Humberto Osorio ensured the spoils were shared.
The result marked Real's second successive draw, which Ancelotti attributes to them having played 10 matches since the start of April as they bid to conquer Spain and the UEFA Champions League.
"Physically we are not tired," said the Italian. "But mental tiredness cost us. After such a Champions League semi-final it's not easy to recover quickly at such an important tie of the season.
"We were in control for 70 minutes, but we lost control, sat back and conceded a goal from a set-piece."
The result leaves Real four points behind leaders Atletico Madrid, and one behind second-placed Barcelona, with two rounds remaining.
Ancelotti nonetheless maintained that his side will keep fighting for La Liga.
"It will be very difficult but it's still possible mathematically," he said. "We have to win our remaining two games. I don’t care who are the favourites."
