The veteran Socceroo was booked for tangling with Jara before the break after heading in his team's only goal in the 3-1 Group B loss to the South Americans.
Coming off at half-time he was seen arguing with Chile's Arturo Vidal, and later explained the nature of that altercation with the Juventus star.
"There was an incident where the left-back (Jara) elbowed me and kicked out at me when I was trying to run past him for a cross, and I've got the yellow card," Cahill told Australian media.
"I said to Vidal, 'This is no good, this needs to be out of the game.'"
Australia started disastrously and were two goals down before the quarter of an hour, but a Cahill-inspired turnaround saw the Aussies finish strongly, with the former Everton star even getting a second goal only for it to be disallowed for offside.
They now head for a clash with table toppers Holland, while Chile face Spain, crushed 5-1 by the Dutch, in Rio's Maracana stadium on Wednesday.