United are top of the table after substitutes Marcus Rashford and Marouane Fellaini scored in the final 20 minutes against stubborn opponents.
At one stage, it looked as if Leicester would hold on for a point, with their goalkeeper Kasper Schmeichel saving a penalty from Romelu Lukaku early in the second half.
Mourinho admitted that he missed Rashford’s opening goal as he was giving instructions to Jesse Lingard, who was about to come on as a substitute.
But in discussing that moment, the United manager also expressed surprise that a crowd of 75,021 fans did not make more noise.
He said: “I didn’t see the first goal. I was speaking with Lingard because Lingard was going to be the next player to come in.
“I saw the ball in the net and all the guys jumping around. It was the first time I saw the crowd. They were very quiet today.
“It was easy to know that was a goal because it was the first time I really understood the stadium was full.”
United have won all three of their Premier League matches so far, scoring 10 goals and conceding none.
They also appear to have developed a more ruthless streak, having drawn 15 league matches last season as they finished sixth.
Mourinho believes his players deserve credit for subduing a Leicester side who had scored five times in their first two matches, losing 4-3 at Arsenal before beating Brighton and Hove Albion 2-0.
– ‘Control’ –
The visitors’ England striker Jamie Vardy had few chances to impress as United centre-backs Eric Bailly and Phil Jones marked him out of the game.
Mourinho said: “We didn’t have many matches last season where we played 90 minutes with the control we had today.
“Vardy is a very dangerous player. I would say he is one of the most dangerous players in the Premier League.
“Was he dangerous today? No. Why? Because we played so well to control them.
“Were Leicester very dangerous against Arsenal? Yes. I watched the match many times. Were they dangerous against us? No. Why? Because of us. So we had a very good and solid performance.
“After the penalty, when you miss a penalty with half an hour to go, normally there is always a little collapse, and that didn’t happen. We kept creating chances and getting corners, and in the end it was from a corner that we scored.”
Leicester manager Craig Shakespeare felt his players performed well in frustrating United for large parts of the game.
But having conceded the goal that lost them the game at Arsenal from a corner, he was disappointed that his players once again fell behind from a set-piece.
At Old Trafford, it was a Henrikh Mkhitaryan corner that was diverted in by Rashford for the opening goal, and Shakespeare warned that it must not become a habit.
He said: “It’s a set-play. We need to be mindful that it doesn’t become an Achilles heel for us.
“We spoke about it after the Arsenal game and we worked on it, but we have to put it into action as well.
“We knew we would have to frustrate coming here. For large parts of the game, I thought we did that and did it really well.
“We knew they would have their moment. And the big moments, they managed to capitalise on.”
Download our app and read this and other great stories on the move. Available for Android and iOS.