Ifill, an English-born Barbados international, said he was racially abused by a spectator on Sunday at Adelaide's Hindmarsh Stadium.
Football officials are working with police and the club to identify the culprit and FFA chief David Gallop promised tough action against such fans.
"Fans must know they'll get banned if they engage in that type of thing," Gallop said in Sydney.
"Football wants to celebrate its multiculturalism, its diversity and that kind of taunt is something that's not on.
"We've seen overseas there can be criminal sanctions in relation to that. At this stage it's dealt with as a ban and those bans must be taken seriously.
"You can expect a knock on your door from police if you engage in that type of behaviour."
Gallop hoped that Sunday's incident was an isolated one and called on fans to help stamp out racism from the sport.
"We have to remember that was a very small minority of people that misbehaved," Gallop said. "But our fans need to know we take seriously those issues.
"It's an issue we need to stay vigilant about and we need our fans to stay vigilant about.
"If our fan groups can regulate that kind of thing then we're a good chance of stamping it out."
Adelaide captain Eugene Galekovic also voiced his support for strong action against racism.
"I don't condone racial sledges or anything like that ... there is a line and you can't really cross that line anymore," Galekovic said.
In a statement on the club's official website, Adelaide said it was assisting with the investigation.
"Adelaide United FC does not condone the reported spectator behaviour," it said. "The club is assisting stadium management and Football Federation Australia with its investigation and will support any sanction imposed on the guilty party.
"Adelaide United FC conveys its concerns to Paul Ifill, as this incident does not reflect views or expectations of Adelaide United FC or any Hyundai A-League club."
In another incident at the weekend, three Western Sydney Wanderers fans were arrested for throwing flares onto the Allianz Stadium pitch during Saturday's derby against Sydney FC.