Mackay remains at odds with club owner Vincent Tan, though talk of his dismissal has been shelved in the past 48 hours.
Moyes said: "I certainly have sympathy for Malky Mackay. It certainly can’t be a decision about football because he has done everything correct with the football team. He has prepared them right, he got them into the premier league, he has made them competitive, he has a stadium and crowd right behind the team.
"What any manager wants to do is improve that and he recognises that if he doesn’t continue to improve Cardiff then it could be tough. I don’t know what goes on behind the scenes but I can tell you that it has nothing to do with football. He is doing a great job.
"Stability brings success and it is the best way for managers. Not always the way clubs go but from my experience my bosses have all believed in stability and I certainly do too."