Palace trailed 2-1 with seven minutes remaining and were in real danger of missing out on a play-off spot before an equaliser from substitute Kevin Phillips and Jedinak's header from Stephen Dobbie's freekick saved them and broke Posh hearts.
The late double strike gave Palace a 3-2 win and means they will now face bitter rivals Brighton in the two-legged play-off semi-final.
For Ferguson, it was a bitter pill to swallow as Barnsley's point at Huddersfield saw Posh drop into the third tier after two seasons in the Championship despite finishing with 54 points.
"It's difficult to explain how we feel as a group," said Ferguson. "It couldn't have gone any closer.
"The only person you don't want the ball to fall to is Kevin Phillips because he's a born goalscorer.
"At 2-1 there only looked like one winner. To lose the goal we did - you need luck in this game and we just haven't had the luck.
"Someone has to suffer and unfortunately it's us. I'm just devastated for my chairman and for my players."