Arsenal earned a 3-1 victory over the La Liga side, who are attempting to identify the supporters involved in the incident.
"(Valencia) publicly condemns and expresses its firmest rejection and zero tolerance for, as it has always done, the isolated gestures from people in the away end which evidently do not represent Valencia's supporters," said the Spanish club in a statement on Friday.
European football's governing body UEFA said they were in the process of reviewing reports from the game.
"These blatant racist gestures are shocking and inexcusable," said British anti-discrimination group Kick It Out in a statement.
"We hope the relevant authorities identify the perpetrators and take the strongest possible punishment. There is no place for any form of discrimination in football or society."
(Reporting by Rik Sharma; Editing by Christian Radnedge)
