Rashford was fouled in the box by Moussa Sissoko shortly after half-time, with England international converting the penalty to make the scores 2-1.
Speaking after the game, Mourinho thought Spurs were in control up until that point and was frustrated to concede.
He told BBC Sport: “We started the second half with a goal that it is impossible to concede.
“We were not alert, sleeping at the throw-in and we let [Marcus] Rashford attack. Once he is inside the box it’s more difficult to defend and he was clever and waited for the touch.
“In the first half they started more aggressive and more intense and deserved to be in front, maybe even 2-0, then we took control of the game.
“The goal at the start of the second half gave United the chance to play the way they did.”