The former Hibernian forward is the subject of both a police investigation and a notice of complaint issued by the Scottish Football Association to be heard on May 22 over alleged racist singing in a public house. However, Strachan is relaxed about picking the 23-year-old for a match that takes place on May 28 at Craven Cottage.
"We're a bit sensitive in Great Britain at the moment," he said. "I suppose if you could put a tax on stupidity then it might have cost him a few bob. He would be a very poor man," he added of the striker.
It is understood that any SFA sanction on the charge if Griffiths is found guilty would not include a ban and is likely to be a fine or a censure.
Strachan said: "I've no concerns. I'm glad it's not retrospective because I used to go to Hibs games and sing silly songs as well when I was a kid. He does not change. He is an enthusiastic wee fella all the time."
Strachan also alluded to the controversy over the tax affairs of singer Gary Barlow when he said: "Even Gary Barlow has taken a bit today. He was meant to be a sir last week now they want him to send his OBE back. How ludicrous. If all the world was like Gary Barlow it would be a better place."