The Foxes head for the Stadium of Light on Saturday sitting just two points above the relegation zone after a testing start to the defence of the title they claimed in such remarkable circumstances last season.
However, Moyes believes now that Claudio Ranieri's men have secured their passage to the next stage of the Champions League, they will turn their attention to matters at home.
He said: "I think they have probably had a bigger focus on the Champions League, and it's shown.
"They have done a great job in the Champions League
I think when they saw the draw, they really thought, 'We have a realistic chance of getting through here'.
"But when you are playing Saturday, Wednesday, Saturday, Wednesday and the quality of the games you are having to play in midweek and the level you're having to get to, it makes it very difficult to play again on the Saturday.
"Until you become a really top team which is used to playing in a Champions League game on a Wednesday night and a Premier League game on a Saturday, it becomes tough.
"But Leicester have qualified now, so they have done that bit and they will probably now try to turn their attention to climbing the table - hopefully not this week."
Leicester's triumphant campaign was the stuff of fairy tales, but also showed so-called lesser clubs what might just be possible.
Moyes said: "First of all, it's a remarkable achievement and it's something we'll talk about for years
Everybody who wasn't a supporter of one of the big three or four clubs last year probably were willing Leicester on all the way.
"But what it's actually done is put pressure on many more clubs now
It will not change - if you are at one of the big clubs, the level of scrutiny to win the Premier League is every year.
"But I think there will be a batch or another 10 or 12 teams now where the owners could be saying, 'Well, why could it not be us?'."
The Black Cats' aims for the season are once again far more fundamental as they attempt to stave off another relegation fight against the backdrop of speculation that owner Ellis Short is ready to offload the club.
However, Moyes insists he and the players will not be distracted by the rumours.
He said: "No, no
I got it every sixth months or every year at Everton, we were going to be sold, we were going to be this
Did it ever affect the players? Never
Will it affect the players here? No."
Meanwhile, midfielder Lynden Gooch was consulting a specialist in London on Friday over an ankle injury which is likely to sideline him for up to 12 weeks.
Source : PA
Source: PA