Moyes was appointed by Sociedad 12 days ago and his team looked well organized throughout a fairly scrappy game at Estadio Riazor.
The visitors had the better of the first half and ex-Arsenal man Carlos Vela had a dipping shot saved by Fabricio before putting the best chance of the first period over the crossbar.
Moyes was also a bystander in a bust up between the two benches, and a member of the Deportivo coaching staff was subsequently sent to the stands for taking his protests towards the referee too far.
Deportivo were far more aggressive after the break and would have been in front had Pablo Insua made a better contact when he met a corner at the far post.
Vela did have a final chance to put Sociedad in front but he fired into the side-netting on his weaker right foot 15 minutes from time.
And Sociedad goalkeeper Enaut Zubikarai then had to be alert seven minutes from time, doing well to keep out Juan Rodriguez’s low effort and ensure Moyes??? side returned to San Sebastian with a point.
The 51-year-old Moyes has only just started learning the language and mostly had to rely on an interpreter to communicate with his players.
“The coach has asked us for more intensity and I think we showed that in the first half when we created some good chances,” Sociedad midfielder Sergio Canales said in an interview with Spanish television.