Blatter suggested that racist abuse between players should be settled by a handshake - and McCarthy said the FIFA president's remarks were so appalling he should step down.
McCarthy said: "They are outrageous comments from Blatter. I would expect better from a man heading that organisation, that's for sure.
"It is doubtful whether he can remain. I say doubtful but he runs the place. He has got to resign if he is going to go.
"Whether he has got that about him, I don't know. He shouldn't have said it.
"I think he should go personally. His comments were barmy and at best misguided."
Birmingham defender Curtis Davies labelled Blatter's remarks as laughable.
He said: "If someone calls you this and that due to your race, you know they've dug deep to say that to you.
"It's just laughable really to think that you could shrug off being called whatever with a handshake."
Tottenham assistant manager Joe Jordan said that racial abuse crossed the line of what should be left on the pitch.
"You have to accept there is banter on a football pitch," said Jordan.
"But there are lines that are banter and there are lines where you have to say 'you can't say that', and when that happens it can't be forgotten at the end of a game."
Lord Herman Ouseley, chair of football's equality group Kick It Out, was left stunned by the comments made by Blatter in two television interviews.
Ouseley said: "To say Sepp Blatter's comments are unhelpful is an understatement. They're disbelieving.
"He has no understanding of what racism is, the ideology behind it, the damage it causes and how it subjugates one group of people as inferior.
"Enlightened leadership at this level is needed. Minor matters on the field often can be resolved with a handshake. Racism is not a minor matter.
"Kick It Out has no truck with the notion that racism can be dismissed and trivialised in this way."
Preston defender Clarke Carlisle, the PFA chairman and a Kick It Out ambassador, warned that Blatter's comments run the risk of undermining years of work aimed at eradicating racism from the game.
"We've come through some 20 or 30 years of campaigning to bring racism to the height of awareness that it is at the moment,'' he told BBC Radio 5 Live.
"To come so far on such a sensitive topic, [yet] in one fell swoop he can almost give carte blanche that racism is acceptable between the hours of 3pm and 4.45pm on a Saturday."
The 20 Premier League clubs released a statement on the issue following a meeting of club chairmen.
The statement said: "The English game has been at the forefront of tackling racist behaviour and other forms of discrimination.
"Everybody in the game in England understands any form of racism is totally unacceptable.
"There are still issues, as there are in society, so with our partners, Kick It Out, the PFA and the FA, we must remain committed and vigilant to maintaining the standards we have set and confronting any incidents that occur."
Stoke boss Tony Pulis was another manager amazed by what Blatter had come out with.
Pulis said: "I think one thing it proves is that he is miles away from what is actually happening in football and in the world. I'm amazed that he has come out with the comments, but the big question is who is actually going to take him to task."
Former Sheffield Wednesday and Crystal Palace striker Mark Bright warned that the effects of the comments could be felt throughout football.
Bright said: "This is what Blatter is saying: at Hackney Marshes on Sunday morning you can say whatever you want to your opponent, whatever race, creed or colour he is, and at the end of the game when you shake hands it should be all forgotten - go to the bar and have a drink. Those days are over. It's an old-fashioned view, it's archaic, it's illegal."