"Certainly I don't have confidence in Mr Infantino, after this point, given what transpired," Carney told reporters when asked about FIFA's chief and his now-shelved plan to open the World Cup up to private investment.
Infantino has come under increasing pressure, even from within his organisation, over his handling of the proposal, and calls for him to step down have grown since he abandoned it last Saturday.
Carney said Infantino's reported failure to discuss the plan with FIFA's senior management team "should be fatal" to his tenure leading world football's governing body.
"This is not how you run any business, a small business, let alone something that is a global responsibility like football," Carney told reporters in Toronto.
Infantino held emergency talks earlier Wednesday with FIFA directors in Morocco, the 2030 World Cup host, seeking to contain the crisis.
Infantino had been basking in the afterglow of a highly successful World Cup, the largest ever with 48 teams and co-hosted by three countries: Canada, Mexico and the US.
But his tenure is facing an unprecedented threat amid a wave of global fury over the scrapped plan, which called for the creation of a new commercial subsidiary, called the FIFA Forward Enterprise, to run events such as the World Cup.