With only a few minutes gone defender Amartey handled in the box and Pogba, after a stuttered run up, hit the ball over Schmeichel into the top of the net.
He also said he'd moved past the excitement of the summer, adding: "Winning the World Cup is in the past".
Nonetheless Mourinho was pleased with his team's display, singling out Pogba and Shaw for particular praise, and the overall spirit.
"We have big coaching staffs and I think we are more the head coach than the manager".
"I'm not thinking about that unavailable list I give you, I focus on what we have".
Leicester manager Claude Puel: "We lost Riyad Mahrez, who was a very valuable player for us, so it was important to keep our best players and have good additions to the squad".
However, United saw out the rest of second-half stoppage time to start the season with three points and maintain Mourinho's unbeaten record in Premier League openers with nine wins and one draw over 10 matches.
Boateng trained with Bayern Munich on Thursday, with Paris Saint-Germain now touted as the front-runners for his signature - a deal that can, of course, be done later in the month after the Premier League bows out of the market as a buying power. "We will have the same players, the injured players are not going to be back", said Mourinho.
"That's football, that's football management, I think football is changing and probably football managers should be called head coaches".
"We should start the Premier League with a win and we did", he said.
The two-time Champions League victor added: "At this point I'd just say we need to win".
Having had a full pre-season behind him, undisturbed by the World Cup, Alexis Sanchez should have come into this game like a house on fire.
"I had only two options, Scott [McTominay] or Paul, but if I play Scott I play two two kids and a new player, so I asked Paul and he put himself available for the team and he was very, very good for us".