Mourinho's side were seconds away from a win that would have kept them in touch with Premier League leaders Manchester City.
After falling behind to Jamie Vardy's strike, United led through Juan Mata's double, but the visitors switched off in stoppage-time and Leicester's Harry Maguire snatched a dramatic leveller.
United are now 13 points adrift of City and Mourinho was furious with his team's late defensive blunder and a series of woeful finishes when chances arose to kill the game.
"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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"We were punished by our mistakes. Childish loss of possession, so easy. Childish in their box and childish in our box. We were punished in two points."
It was another frustrating day for Mourinho, whose side had crashed to an embarrassing League Cup quarter-final defeat at second-tier Bristol City in midweek.
Asked how he felt after United's latest mishap, Mourinho said: "I feel great. The reality is that it is 2-2.
"It was an easy match to win, we did everything to win but when you lose big chances.