The 20-year-old England worldwide scored both goals for United in their 2-1 victory over arch-rivals Liverpool at Old Trafford this weekend.
De Boer lost all four of his Premier League games without scoring a goal before he was sacked by Palace in September.
"I read some quote from the worst manager in the history of the Premier League, Frank de Boer - seven matches, seven defeats, zero goals", said Mourinho, alluding to De Boer's unsuccessful spell in charge of Crystal Palace earlier this season.
"He said it wasn't good for Marcus Rashford to have a coach like me because the most important thing for me is to win".
Maybe with him, he would learn how to lose.
"'It's a pity that his manager is Mourinho because you want to give him time and he can make mistakes".
CM Punk Teases Return to the Octagon at UFC 225 in Chicago
His one and only fight to date ended in disaster that night, as he was steamrolled by the younger, more talented Mickey Gall . Punk, who lives in his native Chicago, immediately said he meant to fight again but has been relatively quiet since.
Furthermore, the signing of Romelu Lukaku has seen the Englishman deployed as a winger on numerous occasions, and De Boer does not believe Mourinho has the patience to allow Rashford the necessary room to develop. "The kid made all the right decisions and they wanted him to make all the wrong decisions".
"I try to give the best to [Rashford]", Mourinho said. I have to be honest and give the credit to the people of the academy that was responsible for his formation, to Louis van Gaal [Mourinho's predecessor] who was responsible for his first season. "I'm really happy with Marcus".
The former Chelsea manager has not just talked the talked though but has also walked the walked as Marcus Rashford was the only player involved in every match-day squad prior to his injury. He plays for United many matches, he starts some comes from the bench for others.
However, those numbers just aren't cutting the mustard with De Boer, who said it was a "pity" that Rashford is playing under Mourinho due to the restrictions the United boss puts on his players. Of course not. He's a player we trust. "I'm really happy with Marcus".