Macclesfield have reported allegations that defender Ryan Jackson was racially abused by a Barrow player during Saturday's FA Cup second-round replay.
There was also an alleged post-match contretemps in the players' tunnel which had to be defused by police and stewards following Town's 4-1 win.
Macclesfield chief executive John Harris said: "We are very disappointed that this has overshadowed an excellent performance, but we remain staunchly opposed to all forms of racism, which we believe has no place in football or indeed anywhere.
"The club are aware that the matter has been reported to both the Police and
the FA and will offer both it's fullest support in dealing with the matter."
The FA is already investigating an allegation that Town captain Nat Brown was
racially abused during the original tie on 19 December.
Manager Steve King said Brown had been called 'a monkey' by some Barrow fans as he made his way out for the second half.