"We need to quickly regroup and focus on the Brazil game".
The defeat represents a huge shock for Australia who must now simply beat Brazil on Thursday to have any chance of progressing, while Italy will nearly surely seal qualification with a victory over minnows Jamaica on the same day.
"I don't think we deserved that", Australia coach Ante Milicic said. "Maybe that calmed us down a bit so we were able to play the way we know how".
Bonansea, however, equalized 11 minutes into the second half after a defensive blunder on the edge of the box.
Bonansea had a goal disallowed for offside in the eighth minute following a Video Assistant Review.
The loss isn't terminal for the Matildas' hopes of progressing in France, but they now need a result in their next match with Brazil in four days time.
Her curling cross was bound for Kerr, who found herself wrapped in a bear hug from Italy skipper Sara Gama with the referee pointing to the penalty spot in the 22nd minute. Goalkeeper Laura Giuliani denied Sam Kerr's first attempt, but could do nothing to her follow-up.
Chloe Logarzo kept her place in midfield alongside Tameka Butt, with Hayley Raso and Caitlin Foord to support striker and captain Sam Kerr. She put a shifty move on a defender before placing a right footed shot into the net.