Former Celtic and Aston Villa boss O'Neill ended 16 months out of the game by succeeding Steve Bruce earlier this month.
Two wins in three games have moved the Black Cats out of the drop zone and Moyes does not think that is a coincidence.
Moyes, whose men face Sunderland on Wearside on Monday, said: "What would you expect Martin to do? You would expect him to come in and make an improvement. He has already done that.
"It is the mark of a really good manager, someone who can come in and make a difference right away."
Moyes, in charge at Goodison Park for a decade, believes O'Neill's recent break from the game has likely been a bonus.
"I think once you have been out of it and you come back, you are full of it.
"No matter what job you are in, if somebody says you can have a break and you don't need to work, when you come back it is great, I am sure.
"It has suited Martin. I am not saying it would suit me or anyone else."
Everton are currently only three points clear of their rivals but have a good record against Sunderland, having not lost in their 13 previous meetings, winning 10 of them.
With the transfer window looming Moyes says his options are limited.
"Agents are ringing up now and some of the names they are putting in are ridiculous - far too much money for players who are well past it or not at the level we expect.
"If we can get someone who can score goals, that is what we need," added Moyes, in recognition that his side have scored just 17 goals in 16 league games.
Sunderland defender Wes Brown meanwhile says the same players who got Sunderland into early-season problems can bring about a resurgence.
Brown scored a late winner at QPR in midweek to lift the Black Cats clear of the drop zone and insists: "We have always had it. The players haven't changed, we have always had it in the team. We managed to get that break on Wednesday night, and hopefully we can carry on from there and have a good Christmas period."
Source: AFP
Source: AFP