England forward Rashford scored two wonderfully taken goals as he starred decisively in United's 2-1 Premier League win over bitter rivals Liverpool on Saturday night (AEDT) – his first top-flight start since Boxing Day.
De Boer, who was sacked as Palace manager last September after failing to muster a goal or a point over the course of four games in charge, said it was a "pity" the 20-year-old had Mourinho as a manager, as the Portuguese would deny him the game time he required.
The United boss had an acerbic response to hand when he addressed a news conference ahead of Wednesday's (AEDT) UEFA Champions League showdown with Sevilla, seemingly holding De Boer responsible for Palace's slump extending to seven winless and scoreless matches as Roy Hodgson picked up the pieces at Selhurst Park.
"I read some quote from the worst manager in the history of the Premier Leauge, Frank de Boer," Mourinho began. "Seven matches, seven defeats, zero goals.
"He was saying it is not good for Marcus Rashford to have to be coached by me.
"If he was coached by Frank he would learn how to lose because he lost every game."
Mourinho went on to credit United's academy staff and his predecessor Louis van Gaal for their role in Rashford's development and insisted the player remains in safe hands under his own leadership.
"We try to give the best to the kid's education. 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.
"If you go to his numbers and how many matches he played with me last season and this season, maybe I am wrong, but I would say he is probably in the top five players with the most matches over two seasons.
"The best thing that can happen for a kid is to have experience and Marcus is having these experiences."
Rashford is set to feature in England's squad for the 2018 FIFA World Cup in Russia and might be granted a more prominent role than expected as Gareth Southgate waits to find out the severity of the ankle injury Harry Kane suffered during Tottenham's 4-1 win over Bournemouth on Monday (AEDT).
Southgate has discussed Rashford's progress with the man at the helm at Old Trafford, and Mourinho insists the England boss is satisfied with the current state of affairs.
"I think that Gareth Southgate doesn't mind that I say a couple of minutes of our conversation were about Marcus," Mourinho said.
"I think we were all on the same page. He [Rashford] played for Manchester United many, many, many times. He starts some and comes from the bench in others. He is 20 years old.
"Does he play every match from the start? Of course not but he is a player that we trust. I said that before the Liverpool match when many of you were maybe not expecting him to start.
"He started and had a good match and I'm not just talking about goals. I'm really happy with Marcus."