The 30-year-old defender, who denies the claims, is waiting for the results of a police investigation.
"We fully back John," said Villas-Boas. "He spoke to Anton after the game.
"For us it was end of story. It's just a big misunderstanding and something blown out of proportion."
Videos circulated on the internet in the aftermath of the game, which saw Chelsea reduced to nine men in the first half, with some claiming the footage shows Terry insulting the QPR defender using racist language.
Ferdinand has yet to make a comment about the chain of events while police are investigating the allegations after a public complaint.
However, Villas-Boas backed the England captain saying: "John is a player who [represents] this country to the highest level internationally. He is a player of great responsibilities.
"I find it strange when people don't trust the words of a representative from your country.
"The clubs are in touch with each other and for us the matter is over.
"We have full backing for our player and for us it is the end of story.
"The rest we have to wait and see."