"Coaches of all teams would be worried about this position but I am not worried," Moyes told a news conference.
"I am here to finish the season and do my work. We need to look at the long-term. I am confident in the players, they know that I support them but they need to show their quality."
It was a poor performance from Sociedad with Jonathan Viera and Sergio Araujo scoring for Las Palmas, and the team is no better off in the table than when Moyes arrived this month a year ago.
The former Everton and Manchester United manager was considered a risky appointment by many critics due to his limited familiarity with La Liga and inability to speak Spanish.
It has, though, been a tough task for the Scot with minimal investment while at the same time, Real have sold important players such as Antoine Griezmann and Claudio Bravo in recent years.
"I am used to dealing with situations like this," Moyes added. "The players and I need to do better and it is a question of everyone working together."
(Reporting by Tim Hanlon in Barcelona; Editing by John O'Brien)
