Striker Cole has admitted the charge and requested a personal hearing after the FA took action over comments he posted on Twitter during the England v Ghana game at Wembley.
The Hammers striker wrote: "Immigration has surrounded the Wembley premises! I knew it was a trap! Hahahaha. The only way to get out safely is to wear an England jersey and paint your face w/ the St. George's flag!"
Cole, whose mother hails from Sierra Leone and his father from Nigeria, later deleted the message and said it had been a joke.
Grant insisted he had no problem with Cole's tweeting and he suggested the FA should have more important things to concentrate on.
"Today there is Twitter, Facebook. Facebook destroyed one government in the Middle East so I don't know what will happen with Twitter," Grant said.
"It is funny sometimes, especially how Carlton is doing it. He is doing it in a funny way. If people like it they can look at it, if they don't like it they don't have to look at it.
"I don't think we need to take it too far. Of course (his apology) should be the end of it. To charge Carlton Cole with racism, I think it was a joke.
"The FA was a little bit in a fight spirit over the last week. They were looking at Twitter, Facebook and what you said to the referee. This is not the main thing."
Grant will be serving the second of a two-match touchline ban against Aston Villa following comments he made about referee Mike Jones.
There is no precedent for allegedly racist comments expressed via Twitter but Grant does not expect Cole to be banned over the issue.
The most likely outcome for Cole is a warning and a fine. The former Liverpool striker Ryan Babel was fined £10,000 in January after re-tweeting an image of the referee Howard Webb in a Manchester United shirt.
The Hammers tackle Aston Villa at Upton Park knowing a victory could take them out of the relegation zone and to within two points of their struggling opponents.
Gerard Houllier has hailed Aston Villa skipper Stiliyan Petrov as "a fantastic leader" after setting his side a seven-point target to ensure Barclays Premier League survival.
Petrov has had to play second fiddle to the Nigel Reo-Coker and Jean Makoun partnership in recent months.
But the Bulgarian international earned a recall for last week's win over Newcastle and Houllier has confirmed he will start at West Ham.
Houllier said: "I left him (Petrov) out when I felt it was maybe good for the team.
"But he showed a lot of commitment and his fitness has improved and he is a great captain also.
"In difficult times you need the people you can rely on and he is one of them.
"He is in my plans. I'm not talking about the past, I'm talking about the future."
Houllier added: "Stiliyan, and all the squad members have demonstrated a lot in terms of effort, quality of effort, application and mentality.
"They have demonstrated they want this club to go up. They feel committed to what we have to do together and Stiliyan has been a fantastic captain and a fantastic leader for the rest."
Victory will take Villa to the 40 point mark - eight clear of the Hammers.
But even then Houllier will still take nothing for granted.
He said: "Going into the Everton game, we viewed it as a mini league of eight games remaining and I'm pleased we've got four points from the first of those two matches.
"But in fairness we may need another two wins and a draw to be safe.
"I think we need a minimum of seven points."