A spectator at Hindmarsh Stadium was heard to call Ifill a derogatory racial term after he was substituted in the 61st minute of the 3-1 loss, the Australian Associated Press reported.
Adelaide United FC said it did not condone the reported spectator behaviour.
"The club is assisting stadium management and Football Federation Australia with its investigation and will support any sanction imposed on the guilty party,'' the club said in a statement.
"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.''
Ifill had no comment today, saying he was instructed by FFA not to speak to the media.
An Adelaide police spokesman said a complaint had not been made with them about the incident.
Wellington Phoenix general manager David Dome yesterday would not comment on the nature of the abuse but said the club were treating the allegations very seriously.