On Saturday, De Boer said it was a “pity” Marcus Rashford was working under Jose Mourinho.
And the Manchester United manager fired back at the Dutchman for his performance with Crystal Palace when he was sacked after five games.
Mourinho said: “I read some quote from the worst manager in the history of the Premier League, Frank de Boer – seven matches, seven defeats, zero goals.
“He was saying that it is not good for Marcus Rashford to have a coach like me, because the most important thing for me is to win.
“If he was coached by Frank, he would learn how to lose because he lost every game.”
But following United’s exit to Sevilla, De Boer has responded to Mourinho’s comments.
De Boer told Dutch outlet Algemeen Dagblad: “I respect him as a manager. He’s won plenty, is tactically very strong and knows how to disrupt his opponent’s game. That’s something I can learn from.
“It has brought some attention, my performance at BT Sport. I meant nothing personal about it, when I said something about how Mourinho plays and about the role that Marcus Rashford has under him at United.
“That way of playing, that is a different view than we are used to in the Netherlands.
“But the philosophy of Mourinho and Manchester United is different. And that is also their right.
“It was also about England and the World Cup. If United buys Alexis Sanchez in the winter break, and then he plays him eight times out of 10 in Rashford’s position, England can suffer at the World Cup.
“Rashford is the greatest English talent in his age group.”