Football Against Racism in Europe (FARE) have contacted world football's ruling body FIFA about the complaints and the Football Association is awaiting official notification of the incident which could lead to England being forced to play behind closed doors.
Rio and Anton, who is on loan from Queens Park Rangers to Turkish club Bursaspor, were allegedly targeted by England supporters in the game in San Marino last Friday.
"You expect and accept banter from fans on the terraces as it's part of what makes the game great but racism is not banter... and from your own fans? WOW," the 34-year-old Rio said on his Twitter account.
"Always a small minority who ruin it for others. Let's not jump to conclusions and assume though as it might just have been banter. We'll see after the investigation."
Ferdinand, who won the last of his 81 caps in June 2011, angered some England fans when he withdrew after being recalled to Roy Hodgson's squad for the match in San Marino and Tuesday's World Cup qualifier against Montenegro that ended in a 1-1 draw.
Hodgson said he did not speak to Ferdinand before naming him in his squad and the defender eventually pulled out, citing a special fitness routine he needs to adopt to help control a long-standing back problem.
After his international withdrawal the experienced player flew to Qatar to work as a TV pundit for the San Marino game.
FERGUSON REACTION
United manager Sir Alex Ferguson said on Friday that he told Ferdinand to go to London to meet Hodgson face-to-face and explain his decision.
Ferguson added he had no problem with the player's trip to Qatar.
"He trained last week then had Friday, Saturday and Sunday off and he could make his own choice about things," Ferguson told a news conference ahead of runaway leaders United's Premier League match at Sunderland on Saturday.
Asked about the alleged racist songs, Ferguson said: "I think that's modern society I am afraid. We see a bit of that from supporters and the way they react to things".
FIFA is obliged to investigate FARE's complaints and if they decide the songs were racist England could be heavily penalised.
Bulgaria and Hungary were forced to play behind closed doors in the last week following earlier cases of racist and anti-Semitic chants at World Cup matches.
It is not unheard of for supporters to turn on their own players and racially abuse them.
Southampton's Poland international goalkeeper Artur Boruc threw a water bottle into a crowd of his own fans this season when they began racially abusing him and said his action cost him a place in the starting line-up for several weeks.
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