The contest at Goodison Park comes less than three days after Spurs' 3-1 Europa League victory over Panathinaikos on Thursday night, for which Villas-Boas fielded a relatively strong starting XI.
Although Moyes feels that will not necessarily have a negative impact on the London outfit in tomorrow's game, he says he would definitely be concerned about the possibility if it was his team.
Asked if he thought fatigue might be an issue for Tottenham, Moyes said: "I think if we had been playing, I would be thinking about that - I'd be saying it is a possibility.
"Does that really happen? I'm not sure. I'm not a great believer that it really happens.
"But if I was the manager, I would certainly be worried about it."
The evidence of recent weeks would suggest that Villas-Boas is doing a good job of balancing European and domestic commitments.
By avoiding defeat in the Panathinaikos game, Tottenham ensured their qualification for the last 32 of the Europa League, and the win came off the back of three straight victories in the Premier League that have taken them into the top four.
It has been an encouraging period for the Portuguese, whose appointment as manager over the summer - following an unhappy stint at Chelsea last term - was met with scepticism by many Spurs fans.
After a slow start to this campaign, Villas-Boas appears to be winning some of the doubters around.
And it has come as little surprise to Moyes to see Tottenham beginning to find their feet under their new boss - particularly given the quality of the players he inherited at White Hart Lane from his predecessor Harry Redknapp.
"They have a really good team," Moyes said.
"It always takes managers time to settle in, but when you are left with an array of players like Tottenham have got, then you are always going to be very close to the top of the league.
"Tottenham have always been there or thereabouts. They have set the team and the club up to be in Europe, they did great in the Champions League with Harry a couple of years ago and this year they have done well to qualify for the next stages of the Europa League.
"Tottenham are one of the clubs you always see as competing at the top end of the league."
Everton, who have drawn seven of their last nine fixtures and are three points behind Tottenham, could have Kevin Mirallas and Seamus Coleman back available for Sunday's match.
Moyes says forward Mirallas, who has missed four games due to a hamstring injury, and full-back Coleman, sidelined for three by an unspecified problem, have "outside chances" of featuring against Spurs.
Victor Anichebe (hamstring) and Phil Neville (knee) remain on the casualty list.