Real were dominated proceedings early on but Khedira received a second yellow card for shoving Sergio Ballesteros in the 41st minute.
And Levante, who were beaten by Real 8-0 in the Copa del Rey last season capitalised on their numerical advantage by claiming all three points through Arouna Kone's strike.
Speaking after the game, Mourinho expressed his belief that Khedira's red significantly hindered Real's ability to mount an attack, and that Levante were more than happy to sit back and retain possession.
"The match evened out once we were down to ten men," Mourinho told Real's official website. "One of the teams kept defending, and the other wanted to attack but lacked potential to do so. The game ended once they scored.
"We played well in the beginning. Our opponent didn't enter our half of the pitch and [goalkeeper Iker] Casillas didn't even touch the ball."
Mourinho also believed the pitch did Real no favours, and feels his team should have been awarded a penalty.
"We had great chances to score and we failed to capitalise on them because the pitch was in bad shape and Levante defended fiercely.
"We dominated the match at times. There was a clear penalty that wasn't awarded to us and it would have also meant that player's second booking.
"If we had scored and they had been left with ten men, the game would have been different."
Nonetheless, Mourinho is backing his men to bounce back from the disappointment of Sunday's loss.
"All points are important and it's better to lose one game than to draw two.
"Losing is tougher psychologically than drawing a match, but drawing two is worse than losing one.
"We'll be in a better position if we exchange this defeat with a reduced number of draws.
"Every game and every point at stake is important."
On their opponents' performance, Mourinho added: "I don't want to detract merit from Levante, who always do very well when they are allowed to play their game at their stadium.
"I congratulate them for being clever. They know how to waste time and how to not give the ball back. They know this because it's also part of football.
"Our players don't feel comfortable in this sort of habitat and Levante know it."
Real will have a chance to make amends on Wednesday when they travel to play Racing Santander, before they play hosts to Rayo Vallecano at the weekend.