Rashfords injury-time goal secured Manchester United their sixth Premier League victory of the season and saw them move alongside Bournemouth into sixth.
Callum Wilson had given the home side the lead on Saturday afternoon but goals from Anthony Martial and Rashford completed the comeback.
Rashford wasted a golden chance to score for United before his winner and Mourinho said this was one of two reasons he was upset with the England international.
Asked about Rashfords winner, Mourinho said: I was very upset with him before that.
I was upset with the chance he missed. He has to smash it and take everything in the goal.
I was also upset because I think he has to win that run with Nathan Ake.
But, of course, then he scores the winning goal and thats amazing for him and us.
After netting a dramatic late winner for Manchester United, Rashford said: You can say that we just have to improve in the start how we usually play in the end, we just just need to get it right.
The most important thing is the three points, we have had an inconsistent start to the season.
It always helps getting points, like you said weve got a big week ahead.
Mourinho, meanwhile, also blasted his team for their first-half performance against Bournemouth.
We were defensively awful, he said. As a team we didnt press or do any of the week we did in the week.
People watching this game will not believe how hard we worked this week.
The first half was a disaster. The second half was much better. We created lots of chances and deserved to score before the 92nd minute.