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.
Saturday's home defeat to Levante will likely be the final nail in his coffin, although Madrid may delay the announcement until after next weekend's Clásico to avoid going into the game managerless.
Lopetegui sent on Gareth Bale at half-time, but, despite incessant late pressure from the hosts, Madrid were unable to get back on level terms.
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Los Blancos are now on a five-game winless run in all competitions, losing four times in the process.
Mid-table Levante seemed the flawless opponent to face, but with a front-line led by the precocious Jose Luis Morales, the visitors had no intention of playing for a point.
"Right now that (his position) is the last thing that I'm thinking about", Lopetegui told reporters. "I am sure that football will soon start giving to us what it is taking away at the moment".
Lopetegui's future is now hanging by a thread and it isn't being ruled out that he doesn't even take charge against Viktoria Plzen in the Champions League on Tuesday night.
Real Madrid 1-2 Levante: Lopetegui may not last the weekend
Real Madrid reached the worst scoring drought in its history in a 2-1 home loss to Levante in the Spanish league on Saturday . At half-time, there were a scattering of white handkerchiefs - the traditional expression of discontent - but more whistles.
Or does Lopetegui deserve more time at the helm?
"They caught us with a goal when we were doing well". There is serious ground to be made up in league play now with Barcelona four points ahead of Madrid, plus three other teams between the two sides in the standings.
"Some very odd things happened as it sometimes does in football".
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