Marcelo’s goal for Madrid had threatened to launch a comeback at 2-1. But it was a brief illusion. The further three thrusts past Madrid goalkeeper Thibaut Courtois capped a savage period for Madrid who have lost four of their first 10 games in La Liga.
Following the setback on Sunday night, Madrid lie in ninth place, seven points behind Barcelona who returned to the top of the table after the success.
Despite the gap, Madrid skipper Sergio Ramos insisted that the title race was not over. "There are people that would believe, others that wouldn't," he said. "I have won La Liga from 10 points behind. The key to success is to work. Madrid never gives up when it can turn the situation around."
The name of former Juventus, Italy and Chelsea coach Antonio Conte circulates as a replacement for Lopetegui who took over at the Bernabeu in July.
Conte, who left Chelsea in the summer following two seasons in which he delivered the Premier League title and the FA Cup, is renowned for his demanding training regime and his meticulous planning.
While 52-year-old Lopetegui bears the brunt of the criticism, Madrid president Florentino Perez is also under scrutiny for sanctioning the sale of Cristiano Ronaldo and failing to replace him with a proven goalscorer.
"It is not just Julen's fault", said the headline on the front page of Marca, Spain's biggest selling daily.
"We feel we could have turned the game around,” said Lopetegui after the thrashing. “We had chances to equalise and go on and win.
"But it did not happen. There was more bad luck, more injuries and the third goal killed our hopes. The punishment was excessive. 5-1 does not reflect the game."