The former Dutch global had praised Rashford and said it was a "pity" that he plays for Mourinho, who only cares about results, and not a manager who would continue to play him even if he has a bad game or two.
The United boss hit back by describing Frank as the "worst manager in Premier League history" following his failed spell with Crystal Palace at the start of the season, but Ronald has attempted to play down the spat before it gets too personal.
Frank De Boer was appointed Crystal Palace boss on a three-year deal at the start of the season, but was sacked just 10 weeks into the job, having overseen a run of 4 consecutive defeats in the Premier League, without his side scoring a single goal.
It is little surprise De Boer's criticism has seemingly rankled with Mourinho.
"Frank respects Jose a lot and was simply pointing out that, if Rashford was playing for Ajax and had one or two bad games, he would still start the third game".
He's scored against Arsenal, he's scored away at Man City, at home against Liverpool, in the Europa League semi-final, in plenty of other big occasions for United.
"We try to give the best to the kid's education".
"He was saying it is not good for Marcus Rashford to have to be coached by me".
And a crucial aspect of Rashford's immediate impact came from the fact Mourinho took him out of the spotlight for some time. Of course, with Marcus, I have to be honest and give the credit to the people in the academy who were responsible for his formation; I have to leave credit to Louis van Gaal, who was responsible for his first season in the first team.
Rashford scored two first-half goals to help United to a 2-1 victory over their rivals for second place in the Premier League.
"I think that Gareth Southgate doesn't mind that I say a couple of minutes of our conversation were about Marcus", said Mourinho. He was Mourinho's most used player in 2017, with 61 appearances for United in all competitions. "I'm really happy with Marcus".