The incident appears to surround a response from Bardsley to a picture posted by defender Scott Harrison on social networking site Instagram of the tunnel area at the end of Saturday's 1-0 loss to the Cottagers at the Stadium of Light.
Bardsley, via his account which has since been deleted, reportedly replied with the words 'Great opening day. Hahahhahahahahahhaha!!!', prompting a storm of protest from Black Cats fans.
It is the latest fall from grace for Bardsley under Di Canio who was left incensed by the 28-year-old's actions towards the end of last season.
Just a few days before Sunderland's final game of the campaign, a Twitter picture appeared of Bardsley surrounded by B£50 notes following a visit to a casino.
Bardsley then played no part in the 1-0 defeat at Tottenham, and in a further sign of him becoming an outcast under Di Canio, he was not included in Sunderland's Premier League squad list when announced last week.
Bardsley broke his foot while on England Under-21 duty last week, scuppering hopes of a potential move before transfer deadline day.
In light of his injury, Bardsley's only options appear to be a loan move to a Championship club once he is fit, or waiting for January when the transfer window re-opens.