The result saw Barca sack coach Ronald Koeman later in the evening.
The Catalans' captain didn't shy away from blame afterwards, instead putting himself front and centre to take any criticism on the chin.
"I fell asleep," Busquets confessed, discussing Radamel Falcao's goal. "They picked my pocket.
"Then they went on the counter-attack and executed it very well. It was my mistake."
Rayo have enjoyed having Falcao to call upon this season, but the Barcelona midfielder credited them for making the game tough in all areas of the pitch.
"It's a tough place to play and we had to start from behind," Busquets said. "I made a mistake and we paid the price.
"We had chances in the second half, and a penalty. We're lacking in everything: belief, concentration, not making mistakes.
"We're not playing badly, but things are adding up and it's hard when you don't score."
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