The hosts got the victor with a penalty kick converted by Adrian Embarba in the 23rd minute after a foul awarded by video review.
After the game, Zidane told reporters: "I do not know if he's focused on Madrid".
The match was open in the early stages as Jose Pozo came the closest to opening the scoring for Rayo on 18 minutes, but he was denied by Madrid goalkeeper Thibaut Courtois who made a rare appearance under Zinedine Zidane.
Defending his players: "I'll always defend them, but I can't today". Sometimes you can not score but today we did not even create chances, did not play at all. We are not only having embarrassing results for our team, we're embarrassing an historic club. We must be very angry, and I am angry, as our image today was bad.
"I am not sorry, just the opposite", he said.
Future: "We have three games to go and we have to play differently". "I have to live through these hard moments like today". We did not offer anything in the duels or running.
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Authorities said an off-duty Border Patrol agent fired at the shooter as he was fleeing the scene, but didn't hit the suspect. He said: "As you can imagine it was an extremely chaotic scene with people running everywhere when we got here".
Rayo, meanwhile, are up to 19th, six points adrift of safety.
The gap widens between them and Barcelona, whose players had been dancing on the pitch at Camp Nou the night before and posing for photos with their children after wrapping up a fourth La Liga title in five years.
Positives: "We can't taking anything positive away from tonight, no. Nothing".
An apologetic Zidane hopes his team can finish the season strongly, although he accepted they had little to play for. That is the reality of today, we can not play like this.
Not since March 31 has anyone except Karim Benzema, out with a hamstring injury, scored for Madrid, who created precious few chances against a Rayo side that have conceded 62 goals this term.
The build up to the game was dominated by Real's refusal to allow Rayo's top scorer Raul de Tomas, who is on loan from Zidane's side and prevented from facing his parent club due to a clause in his contract, to turn out for the home side.