Former Leeds United youngster Vieira, who played the entire match, was abused by a section of the travelling Roma support during the 0-0 draw at Stadio Luigi Ferraris – Claudio Ranieri's first game at the Sampdoria helm.
"I heard it, but I don't want to talk about it. This happens too often, it shouldn't be this way," England youth international Vieira told Rai Sport after the match.
Roma was quick to respond, taking to Twitter to apologise to the 21-year-old and vowing to ban any supporters found guilty of racist abuse.
"Roma would like to apologise to Ronaldo Vieira for the racist boos he was subjected to," the post read.
"Roma does not tolerate racism of any kind and the club will support the authorities in identifying and subsequently banning any individuals found guilty of racially abusing the midfielder."
Sampdoria responded by tweeting: "We are united in saying no to racism."