The two men go head to head on Wednesday night with both clubs in with a chance of European football next season.
O'Neill saw his side crash out of the FA Cup at the weekend when they lost to Chelsea in the semi-final. Villa also suffered heartache in the Carling Cup final, losing to Manchester United.
The Northern Irishman has not given any guarantees about his future but Moyes feels his managerial counterpart deserves nothing but praise for the way he goes about his business.
He said: "Martin O'Neill is really important to Aston Villa. It is not his position that is in jeopardy, that's for sure.
"To get his team to a cup final, another semi-final and to be challenging for fourth, he has done a brilliant job.
"He has a really good team, who will always score goals because of the way they play. He speaks the truth. He says what he feels.
"I think if you asked most clubs in the country would they like Martin as manager, they would say yes."
Since the turn of the year Everton have been one of the form sides, picking up 28 points from a possible 42.
That string of good results has seen them move to eighth place in the Barclays Premier League table - four points behind Villa, who also have a match in hand.
Asked if tonight's match is a must-win, Moyes said: "It probably is. We have to win our games if we are going to make Europe.
"We have always been coming from behind. We had a poor start. The hard part was having three or four serious injuries, and we've been playing catch-up. We have done a pretty good job.
"We still have a chance of a European spot but we need to overhaul Aston Villa. It is important and we would like to be there.
"We will do everything we can. We might need other people to help us out but if we don't do our job, it does not matter.
"The players are making a decent fist of it and have done well to get us into this position."
Influential midfielder Mikel Arteta will sit out the match as he has failed to recover from the groin strain that caused him to miss the draw with West Ham in their last outing.
Victor Anichebe remains absent with a hip injury but Joseph Yobo returns to the squad following a back problem.