The Italian said fifth-placed Newcastle would approach the game against Premier League leaders City in an extremely confident mood after their 2-0 victory at Champions League finalists Chelsea on Wednesday.
"Newcastle played a fantastic game at Chelsea and I think this game will be more difficult for us," Mancini told reporters on Friday.
"The Manchester United game was at home and we played very well to win 1-0 but Newcastle is away and I think it will be harder."
The two Manchester clubs are locked together on 83 points with two games left to play this season, with City top on goal difference.
Mancini said City would keep a particularly close eye on red-hot Senegal striker Papiss Cisse on Sunday.
"Cisse is incredible," said the Italian. "He scored two fantastic goals against Chelsea.
"He has 13 goals in 12 league games for Newcastle and he's a good player. But not just him, their whole team is playing very well.
"They play to win in every game, they have a good mentality and for this reason I think it will be a good game on Sunday."
Manchester United entertain Swansea City and Mancini dismissed the suggestion that Manchester City would be under more pressure because they play first on Sunday.
"Our players know they have everything in their own hands," he said.
