Antoine Griezmann opened the scoring from the penalty spot on 58 minutes following a controversial VAR-assisted decision, but Aston Villa's Jedinak drew level with a spot kick of his own four minutes later.
"We're disappointed, we didn't have the luck today," Jedinak told BBC Sport. "The second goal was fortunate for them, just over the line. We've got to take the positives, pick ourselves up and go again.
"We knew we had to be right at it from the first whistle, maintaining discipline and focus. We got ourselves back into the game, we felt good. Then they got the goal, we gave it a go but it was not enough.
"I told my teammates that if we maintain that structure and concentration we showed today, let's see where it gets us. I can't fault them, almighty effort today."
Peru face Denmark in Saturday's other Group C match from 5pm BST.