The European champions are notoriously known to have one of the most demanding fan bases and board in world football.
The midweek 1-0 defeat at CSKA Moscow in the Champions League, has now increased pressure on Lopetegui and his team.
Dropped points from Barcelona have given Real chances to pull away at the top of La Liga, but they have failed to take advantage.
This weekend, Real travel to Alaves, who have made an impressive start to the season themselves.
“We don’t analyse what people might think.
“We are working every day on trying to improve. The club’s objectives are still intact and nothing more.
“You have to respect all opinions but it’s logical that at a club like Real Madrid you are always under heavy examination. But we will be judged by what we achieve by the end of the season,” Lopetegui said in his pre-match press conference, when he was asked if he believed his job was under threat.