"Maybe one of the players has a word, a gesture, towards the other which is not the correct one," Blatter told CNN in an interview.
"But the one who is affected by that, he should say, it's a game, we are in a game, and at the end of the game we should shake hands," said Blatter who made similar comments in a separate interview with Al Jazeera.
"On the field of play, sometimes you say something which is not very correct," he added.
"At the end of the game, it is over and you have the next game where you can behave better."
Blatter's comments drew an angry reaction from Manchester United and England defender Rio Ferdinand.
"I feel stupid for thinking that football was taking a leading role against racism," Ferdinand said on Twitter.
FIFA later issued a statement from Blatter saying his comments had been misunderstood.
"What I wanted to express is that, as football players, during a match, you have 'battles' with your opponents, and sometimes things are done which are wrong," Blatter said.
"But, normally, at the end of the match, you apologise to your opponent if you had a confrontation during the match, you shake hands, and when the game is over, it is over.
"Anyone who has played a football match, or a match in any sport, knows that this is the case.
"Having said that, I want to stress again that I do not want to diminish the dimension of the problem of racism in society and in sport.
"I am committed to fighting this plague and kicking it out of football."
BLATTER LEGACY
Blatter told Al Jazeera that racism was not a major problem in the game.
"Racism is if there are spectators, or there are movements of discrimination off the field of play, but on the field, I deny there is racism," he said.
"You may say something to somebody who does not exactly look like you... but at the end of the match it's forgotten.
"After the 2010 World Cup in South Africa, it was my opinion that racism, discrimination has disappeared because that World Cup proved that you can connect people."
Blatter admitted he was annoyed about recent corruption scandals involving members of the FIFA Executive Committee.
"Of course, I am angry and disappointed if members and colleagues of our executive committee are in situations where they have to be suspended or withdraw from their activities," he said.
"The confederations voted or elected them, so I have to take what is there."
Blatter, who has said he will not stand for re-election when his fourth and final term ends in 2015, also spoke of his legacy.
"What I want to achieve is that at the end of my mandates, I could say that football is
