It was the Catalan giant's first defeat to Rayo since December 2002 and ended a run of 13 straight LaLiga victories against them.
Sergi Barjuan has been placed in temporary charge, with Xavi expected to be allowed to leave Al Sadd next week following their clash with Qatar Stars League title rivals Al Duhail.
Asked about the possibility of an impending return to Camp Nou on Friday, Xavi said: "I am focused on my work with Al Sadd and I won't talk about anything else."
Xavi came through the ranks at Barca and went on to provide 184 assists and score 85 times in 767 appearances for the club during one of their most illustrious periods.
He left for Al Sadd in 2014 and finished his playing career there, before taking over as coach and leading them to seven domestic trophies.
Barca faces Deportivo Alaves at Camp Nou on Sunday and is away to Dynamo Kiev in the Champions League three days later.