TV footage showed Betis fans appearing to make racist gestures and noises at defender Paulo, a Brazilian player who is black, as he left the field after being sent off in a 4-0 loss to city rival Sevilla.
Blatter wrote on Twitter on Tuesday that he was "sickened to learn of 'fans' racially abusing a Real Betis player. I condemn their actions."
Blatter added it was "nonsense to fight racism with fines. This has to be tackled by ALL competition organizers."
Betis re-tweeted Blatter's words a day after it had also condemned the actions by several of its fans on Twitter.
"Real Betis condemns any act of violence or racism which goes against the spirit and values the club has always, and will always, represent with a team that has traditionally included players of various nationalities and ethnicities," Betis told The Associated Press in a statement. "Real Betis is certain these are isolated chants that do not identify with its principles or fans.
"The club will start an awareness campaign to speak out against violence and racism and will study measures for combating violent and racist conduct in football, especially regarding fans' behaviour. Once these methods are totally defined, they will be made public," Betis added.
Betis said it was trying to identify the four fans responsible for the noises and chants so it could take the necessary action against them.
The incidents at Betis are not an isolated in Spain, where such scenes have previously occurred including to former Barcelona striker Samuel Eto'o of Cameroon at Zaragoza in 2006.Suggest a correction