Barcelona can cut the gap back to three points by beating Levante at home on Sunday but Atletico Madrid now trail leaders Real Madrid by 13 points.
Eden Hazard could be sidelined for more than a month after suffering a fracture in his ankle while Marcelo might also miss the game against Barcelona, after he sustained a calf strain in training.
Real Madrid face PSG at the Santiago Bernabeu, with Gareth Bale's future in doubt and his standing among the fans perhaps never lower.
Wales managed a 1-1 with World Cup runners-up Croatia on Sunday which left their Euro 2020 qualifying hopes on a knife-edge.
Real Madrid vs Osasuna: Eden Hazard and Gareth Bale were among a number of players rested by coach Zinedine Zidane, with Real Madrid facing seven games in 21 days.
Zinedine Zidane said in July it would be "best for everyone" if Gareth Bale left this summer but it was the Welshman's double that earned Real Madrid a point.
Zinedine Zidane said he believes Gareth Bale will now stay, with the Spanish transfer window closing on September 2.
Zinedine Zidane has made clear that Gareth Bale is not in his plans as he looks to rejuvenate Real Madrid following their miserable season last term.
Gareth Bale has already been told by Real Madrid coach Zinedine Zidane that he does not form part of his future plans at the Spanish giants.
Real Madrid clawed back from two goals down to finish full time at 2-2, and prevailed 3-2 in the penalty shootout dictated by the International Champions Cup exhibition tournament format.
Real Madrid boss Zinedine Zidane said at the weekend the La Liga giants were poised to offload Gareth Bale.
"I did not disrespect anyone, least of all Gareth," a frustrated-sounding Zinedine Zidane said.
Zinedine Zidane said the club were working on Gareth Bale's departure, adding that he hoped it happens soon, "for everyone's sake".
While Gareth Bale would be welcome at a host of marquee clubs, his big salary may prove to be an obstacle for all but the richest teams.
Real Madrid's response to Barcelona winning the title on Saturday night was to slip to a 0-1 defeat at Vallecas and fall 18 points behind La Liga's newly-crowned champions.
Real Madrid were mathematically ruled out of the title race after Barcelona beat Alaves on Tuesday while Atletico Madrid look likely to finish above them too for a second consecutive year.
Gareth Bale departed again to whistles with 14 minutes left, a conciliatory hand slap from Zinedine Zidane offering little consolation as he trudged off.
The victory ends a run of four consecutive home defeats and means Real Madrid reduce the gap to nine points behind Barcelona.