City's Elite Development Squad - who are managed by Patrick Vieira - were led off in the first half of their match with HNK Rijeka in Novigrad, after midfielder Seko Fofana was allegedly taunted.
The match was abandoned and representatives from the Premier League champions are now pursuing the matter with match officials and the Croatian Football Association.
"With all these things there is a procedure in place and a procedure that needs to be adhered to," Kick It Out Professional Player Engagement Manager Paul Mortimer told Sky Sports.
"It is a very, very disappointing allegation and I hope the investigation is full, swift and decisive so no stone is left unturned when it comes to dealing with the situation.
"We've already been in contact with Man City. We've got a strong relationship with the club and we've offered our support to them, as well as the opportunity to meet with the players."
Earlier this year City's efforts to promote equality and diversity were recognised by Kick It Out who awarded them an equality standard.
England and Manchester City Women striker Toni Duggan is also one of Kick It Out's Next 20 ambassadors - a select group of players aged around 20 supporting the campaign's efforts to promote inclusion.
The alleged episode involving France U19 international Fofana resembles an incident involving Waford U19s against Serie B side Latina last December which also resulted in the abandonment of the match.
And former Charlton and Aston Villa midfielder Mortimer says it is difficult for people to appreciate how it feels to be the victim of racial abuse as a young player.
"If what has been reported has indeed occurred then it could be the very first time some of these players have experienced racism in their profession," he said.
"I remember when it happened to me during my career and dealing with that for the first time is difficult.
"You experience a number of different emotions. You're angry, you're embarrassed, you want to cry and it's also difficult to predict how you are going to react."