TV footage showed Benfica's Gianluca Prestianni covering his mouth with his shirt - a common move by players or coaches to prevent anyone reading their lips - while making a comment that Vinicius and nearby teammates interpreted as a racial slur.
Although Benfica defended their winger, European body UEFA are investigating the allegations of discriminatory behaviour during Tuesday's Champions League playoff first-leg which Real won 1-0 thanks to a goal from Vinicius.
Mourinho said Vinicius had incited the crowd with his goal celebrations while adding that the club was anything but racist because the Portuguese team's greatest player Eusebio was also Black.
"Jose Mourinho basically attacks the character of Vinicius Jr by bringing in the type of celebration to discredit what Vinicius is doing. For me, in terms of leadership, it's a huge mistake. It's something we should not accept," Kompany told reporters in a 12-minute response in support of Vinicius.
"On top of it, he mentions the name of Eusebio - to say that Benfica cannot be racist because the best player in the history of Benfica is Eusebio. You know what Black players had to go through in the 1960s? Was he there to travel with Eusebio (to) every away game?
"My dad is a Black person from the 1960s also who made his way. Probably at the time the only option they had is to be quiet, to say nothing, to be above it and to be 10 times better to get a little bit of credit."
Kompany described incidents of racism during his own career, including when he was captain of the Belgian national team.
He also said he had met "a hundred people" who worked with Mourinho and did not have anything bad to say about him, but that on this occasion the Portuguese manager had made a big mistake, despite fighting to defend his club.
"So I know he's a good person, I don't need to judge him as a person. But I know what I've heard and I understand maybe what he's done - he's made a mistake and it's something that hopefully in the future won't happen like this again," he said.