Kylian Mbappé came on as a substitute after an injury layoff and was booed by part of the crowd, as was Vinícius Júnior earlier.
"I've being booed before in my career," Mbappé said. "It's part of it. Sometimes they are not happy."
A couple of banners against president Florentino Pérez were held up briefly before being removed by security officials.
Pérez saluted some of the fans, but at one point he appeared to get into an verbal altercation with some of the team's supporters near the VIP tribunes, according to Spanish media reports.
The match capped a chaotic week for Madrid, who started with an altercation between players in training that led the club to fine Federico Valverde and Aurélien Tchouaméni 500,000 euros ($A816,000) each.
Then came the loss to Barcelona in the clasico on Sunday that allowed their arch-rival clinch the league title. On Tuesday, Pérez called for new elections after saying he was the victim of an "organised campaign" to unseat him.
An edgy Pérez confronted journalists and made widespread accusations in a hastily scheduled news conference.
After Thursday's match Mbappe said coach Álvaro Arbeloa had made him the team's fourth-choice striker.
Arbeloa appeared to be caught by surprise by Mbappé's words and said he didn't know why Mbappé felt like that.
Mbappé, who had been nursing a left hamstring injury, said he was ready to play from the start against Oviedo but Arbeloa decided not to use him.
"I'm 100 per cent fine," Mbappé said. "I didn't play because, for the coach, I've been the fourth-choice striker behind (Franco) Mastantuono, Vini (Vinícius Júnior) and Gonzalo (García). I was ready to start, it was his decision, and you always have to respect it. I'm not angry."
Arbeloa later said he never told Mbappé he was the fourth striker in the squad.
"I don't have four strikers, and I haven't told anything like that to Mbappé," Arbeloa said. "He probably didn't understand me. I don't really know what to tell you. I wouldn't tell him that he's the fourth-choice striker."
Madrid have endured two straight seasons without winning a major title. They were eliminated by Bayern Munich in the quarter-finals of the Champions League, ousted by second-division club Albacete in the Copa del Rey and lost the Spanish Super Cup final to Barcelona.
García put Madrid ahead in the 43rd minute and Jude Bellingham sealed the win in the 79th after an assist by Mbappé, who replaced García in the 68th.
In the fight against relegation, Girona moved out of the drop zone after a 1-1 draw with eighth-place Real Sociedad at home. Cristhian Stuani scored a second-half equaliser for Girona.
Conference League finalist Rayo Vallecano, sitting in 11th place, drew 1-1 at 13th-place Valencia.
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