Rousseff praised Neymar for getting behind his teammate and reiterated that Brazil will "raise the flag against racial discrimination" during the World Cup.
FIFA President Sepp Blatter also commented on Twitter, saying that "what (Alves) tolerated last night is an outrage." He added that there "will be zero tolerance" at the World Cup.
The match referee on Sunday included the 75th-minute incident in his match report, so Villarreal could face a fine.
"Our club would like to express its firm commitment to promoting respect, equality, sportsmanship and fair play both on and off the field and our absolute rejection of any act that is contrary to these principles, such as violence, discrimination, racism and xenophobia," Villarreal added in its statement.
Alves has often been subjected to racist taunts and called fighting racism "a lost war" in January 2013 after segments of Real Madrid's fans abused him with monkey chants during a match. Madrid defender Marcelo, who is also Brazilian, was also recently greeted with monkey chants by a section of Atletico Madrid fans this season.
Former Barcelona striker Samuel Eto'o was convinced not to walk off at Zaragoza in 2006 after fans berated the Cameroon striker with racist chants. Two years earlier, Spain fans at Madrid's Santiago Bernabeu Stadium infamously greeted England's black players with monkey chants during an international friendly match.
AP Sports Writer Tales Azzoni contributed to this report from Sao Paulo.
Follow Paul Logothetis on Twitter: www.twitter.com/PaulLogoAP