But Chelsea came from behind to book a place in the fourth round draw thanks to a first-half equaliser from Mateja Kezman, a cruel Andy Crosby own-goal and an 86th-minute clincher from Eidur Gudjohnsen.
But Mourinho was not surprised at the performance, and was impressed by United's quality of play.
He said: "I know cups. I know the mentality of the small teams and I know the mentality of the big players.
"It did not surprise me at all. I was not waiting for a big performance or a big result, I just wanted to go through.
"I cannot say I am unhappy with my players because I¹m not. For Scunthorpe, it was the game of their lives but it was just one more game for us.
"It is a big difference but I have to compliment them because they play a game of quality not just commitment. They can play football, they have some good players and scored one goal - they could have scored more.
"They defend well and I think they have a good team. I can imagine in their competition, they can win it.
"We did out homework with Scunthorpe. We knew they had enough quality to give us a game. But I didn't have a very strong defensive line-up. Only Glen Johnson was a regular as a right-back. It was the first game for centre-half Steven Watt and the first game for Alexei Smertin as a centre-back.
"It was also the first game for Nuno Morais, who is not a left-back, he is a midfielder. But I am very happy with their performances."