On Thursday, Vinicius urged the European governing body UEFA to take action against alleged racist chants directed at him by Atletico Madrid and Barcelona fans.
Real Madrid have also filed a complaint with the state prosecutor's office over hate and discrimination offences, the LaLiga club said on Friday.
The Brazil international has been a target of racist abuse on multiple occasions while playing in Spain, prompting a series of local and international campaigns, including the creation of a special FIFA anti-racism committee.
"The problem is there, I believe it is. I am not going to change my opinion" on racism in LaLiga, Ancelotti told reporters on Friday.
Vinicius was also racially abused last year while playing at Valencia. Several were arrested after that incident, and Valencia banned four people for life.
"I think Valencia responded very well after their episode (with racism). It is others who have to act now. When we talk about zero tolerance, it is for us and for everyone," Ancelotti said.
"I think it is necessary to act and eradicate these problems. They are very ugly things that affect everyone in our society. Criminals (who perpetuate racism) should not be out on the street, they should be somewhere else."
Brazil will play a friendly match against Spain at the Bernabeu on March 26 as part of an anti-racism campaign in support of the Real Madrid forward.
