Posh twice led at Selhurst Park but suffered late heartbreak as goals from Kevin Phillips and Mile Jedinak consigned them to League One.
"It's difficult to explain how we feel as a group," said Ferguson. "It couldn't have gone any closer."
Lee Tomlin gave Peterborough the lead on 28 minutes but they were pegged before half time after Glenn Murray converted a penalty.
Ferguson's side retook the lead on 63 minutes but Phillips pounced with eight minutes remaining, and Palace's comeback was complete when Jedinak headed home Stephen Dobbie's cross in the last minute of normal time.
"The only person you don't want the ball to fall to is Kevin Phillips because he's a born goalscorer," said Ferguson.
"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 today.
"Someone has to suffer and unfortunately it's us today. I'm just devastated for my chairman and for my players."