Marco Asensio had put Real Madrid ahead early, but Levante went on to win the clash with goals from Jose Luis Morales and Roger Marti.
Real were hardly helped by a ninth minute red card to Brazilian centre-back Eder Militao, who was starting due to Sergio Ramos being out injured.
We’re not going to discuss refereeing decisions, you guys are there to assess what happened and have opinions,” Real assistant manager David Bettoni said.
“It’s the way it goes. Levante won 1-2. We’ll take away how we played, which wasn’t easy with ten men because Levante are a good side.
“I saw a Real Madrid full of character, full of pride. We weren’t able to win this game in the second half, that’s all there is to it.
“In the second half, playing with a man less, we pressed high up, signaling our intentions. We couldn’t get the win, but the effort from the players was evident until the end. We’ll take that away with us.”
The defeat comes after Real were surprisingly knocked out of the Copa del Rey by Segunda B club Alcoyano, while they also lost the Spanish Super Cup final to Athletic Bilbao earlier this month.
Real had an unconvincing UEFA Champions League group phase too and with their title defence on shaky ground, the pressure is mounting on boss Zinedine Zidane.
Real goalkeeper Thibaut Courtois said there was still a long way to go in the title race.
“We always have to fight, La Liga goes on until May, but they keep winning and stay at the top,” Courtois said.
“We have to look for a reaction, win our games and make sure the others lose. We had to fight today, we went down to 10 men from the seventh minute and in the end that make football difficult.
“Levante are on a good run, they play good football and always make it difficult, and if you’re playing with 10 men it makes it even more difficult.”