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Juan Mata’s double had turned around Jamie Vardy’s opener and it seemed that United would hold on to their win.
But Foxes defender Harry Maguire volleyed home an equaliser with virtually the last kick of the game.
Manchester City are now 13 points clear at the top of the table following their 4-0 thrashing of Bournemouth today.
And Mourinho was left furious following his team’s display at the King Power Stadium.
He said: "We didn't win because missed incredible chances. I would say joke chances.
"We made a big defensive accumulation of mistakes in an easy match to win. I talked to the players at half time when it was 1-1 that it was an easy match to win.
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“Childish loss of possession, so easy. Childish in their box and childish in our box”
Man Utd boss Jose Mourinho
"The reality is that it is 2-2. Sometimes you make mistakes and are not punished by that.
"We were punished by our mistakes. It was an easy match to win, we did everything to win but when you lose big chances.
“Childish loss of possession, so easy. Childish in their box and childish in our box. We were punished in two points."
Leicester hero Maguire said: "Last minutes goal to equalise, that massive for us. They had chances to kill the game but Kasper Schmeichel pulled out a few saves for us.
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"We had to stick with it, it was crucial to stick with it at 2-1 and thankfully I put he chance away.
"I had a chance in the first half too but I could not bring it down, when I scored there was no way I was trying to control it.
"It feels like a victory but it is only a point against a good side. We need to gain momentum for the next game.
"The manager has come in and results have picked up. We bounced back from the Crystal Palace result but we need to improve in areas to push further up the table.”