Chelsea’s Ji So-Yun rifled an unstoppable drive into the top corner of the Matildas’ net as stoppage time approached to end Tony Gustavsson’s side’s hopes of glory.
Kennedy played the full 90 minutes in the heart of the defence, while Raso was brought on as a late substitute as her nation searched for an elusive equaliser.
Australia dominated the early exchanges with their first chance seeing tournament top scorer Sam Kerr clip an effort off the top of the crossbar.
The Chelsea forward was equally close to breaking the deadlock before the 20-minute mark, heading a Steph Catley corner against the woodwork before South Korea cleared the danger.
But it was the Koreans who were presented with the best opportunity of a frantic first half when former City forward Lee Geum-Min was brought down by Caitlin Foord inside the area.
Captain Cho So-Hyun stepped up to do the honours but blazed her penalty high over the bar to ensure the two sides went in level at the break.
Korea were quicker out of the blocks following the restart, with Matildas' goalkeeper Lydia Williams twice called into action in quick succession.
First she was on hand to deny Lee from point blank range after the forward had stolen a yard inside the area, before tipping Cho’s diving header which looked destined for the bottom corner past her far post.
It was yet another indication that Gustavsson’s side weren’t going to have it all their own way, but they were incensed not to be awarded a penalty of their own when Catley was pulled back inside the area by Cho.
Another gilt-edged chance went begging when Kerr fluffed her lines around the penalty spot, before Korean stopper Kim Jung Mi intercepted a Kyah Simon cross at the vital moment with Kennedy ready to pounce.
And Australia were made to rue those chances when Ji raced into the penalty area and found the top corner of Williams’ net as stoppage time approached.
In an attempt to rescue the tie, Gustavsson rolled the dice and introduced Raso to the fray, but it was Kerr who once again went closest when her half-volley flashed just wide late on.
But it was to no avail, with the Matildas out at the last eight stage of the Asian Cup after falling the wrong side of a pulsating match in Pune.