Referee Simon Mather spoke to the 23-year-old after his attention was drawn to comments made from the crowd during the first half of the game, and U's head coach Hayden Mullins later revealed the nature of the incident.
Mullins told BBC Essex: "I've heard what it is. I've heard at half-time that he has been racially abused and it's not nice, what's been said, especially after we take the knee at the beginning and that was applauded.
"To hear that - there's a section of fans where you hear it from - it's embarrassing, really, to think we're in this day and age and that's still going on. It's sickening, really.
"He said there was a cluster of people and he's looked into the crowd and he's getting racially abused. You think it's 2021 - for God's sake, we should be moving on from that.
"He's reported it and rightly so. Hopefully it gets dealt with and hopefully the person gets the reprimand that he deserves."
Barrow promised a thorough investigation and vowed to take "the strongest action possible" against anyone found guilty of racism.
A statement on the club's official website said: "We are aware of an allegation of racist abuse being directed at a Colchester United player during Friday evening's Sky Bet League Two fixture at the Dunes Hotel Stadium.
"The club would like to make it absolutely clear that we abhor discrimination in all its forms and will take the strongest action possible, including pursuing life bans, for anyone found guilty of racism.
"We will be conducting a thorough investigation and would appeal to any fans who may have witnessed any discriminatory abuse to please come forward and help us identify any perpetrators."