Marcelo's strike with 20 minutes remaining kept Madrid's hopes of a recovery alive, and confirmed the club's longest run without a goal in all competitions in their 116-year history at 481 minutes - surpassing the previous record barren run of 464 minutes set in 1985.
Club president Florentino Perez went down to the dressing room after Saturday's loss to Levante and spoke for 15 minutes with Lopetegui before also speaking to Sergio Ramos who has publicly backed his coach.
Laurent Blanc and former Madrid players Guti and Michael Laudrup are other names believed to have been under consideration if Lopetegui is sacked.
The former Spain boss replaced Zinedine Zidane in the summer but Real are fifth in the La Liga table after a awful start to the season.
And fans have now expressed their indignation on Twitter, with manager Julen Lopetegui now under serious pressure at the club.
Real Madrid are now on a five-game winless run in all competitions.
When asked about the possibility of being sacked after the game, the coach told reporters, "Right now, it's the last thing on my mind", the Coach said after the game. "But we have done a lot of good things, we have to keep trying".
"I am just thinking about lifting them for the important Champions League game on Tuesday [against Viktoria Plzen] where we can turn this dynamic around".
Lopetegui started with Mariano Diaz and Lucas Vazquez in the attack, with Bale and Benzema entering the match in the second half but not being able to help much.
"We have to sit down and think hard about what we are doing wrong and change our path". The ball is not going in.
"Some very odd things happened as it sometimes does in football".
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