Colchester boss Hayden Mullins says it is "sickening" that U's goalkeeper Shamal George was allegedly racially abused during their match at Barrow.
The alleged incident occurred during the first half of Friday's League Two game, which Colchester won 3-2.
"It is embarrassing to think we are in this day and age and that is still going on," Mullins told BBC Essex.
Barrow said the club would investigate and take "the strongest action possible" against any guilty parties.
"The club would like to make it absolutely clear that we abhor discrimination in all its forms," a statement on their website read.
"[We] will take the strongest action possible, including pursuing life bans, for anyone found guilty of racism."
The Cumbrians have called for any fans who witnessed any discriminatory abuse to help identify the perpetrators, and Colchester commended Barrow for their swift declaration to take action.
"Colchester United support Barrow's intention to find and punish any person or persons responsible," a club statement said.
"Colchester will do everything we can to assist their and any subsequent English Football League or criminal investigation into this matter.
"No person, in football or in our wider society, should have to be subjected to this discrimination or abuse and we will support Shamal in any way that he needs it."
Mullins spoke about the incident involving George during his post-match interview with BBC Essex.
"I've heard at half-time he has been racially abused and it's not nice what has been said - especially after we took the knee at the beginning and that was applauded," Mullins said.
"We're in 2021 and we should be moving on from that. It's sickening really."
Mullins praised the 23-year-old, who joined Colchester from Liverpool in August 2020, for his reaction to the incident.
"It's strange that you come away from home and there is not much in the game and then they feel they can racially abuse someone for just being on the opposition team," Mullins said.
"The pleasing thing for me is that Sham did the right thing, reported it and then got his head back in the game.
"Hopefully it gets dealt with and the person gets the reprimand they deserve."