"It was unbelievable and I feel for the 2,000 Bluebirds fans who were there," he told the Echo.
"We let them and ourselves down. We are devastated - and embarrassed about it.
"It was a team failure in the second half and every player accepts blame for it. We cannot defend our position."
Rae could be out for a couple of weeks meaning a changearound in midfield. With no Steve McPhail and Riccy Scimeca now retired Jones will probably introduce Kelvin Etuhu to join Burke, Ledley and Whittingham across the middle of the park.
"Four goals up and we threw it away, we can't blame anybody else," Rae continued. "To play the way we did in the first half and then let it all slip away is embarrassing. Now the players have to focus on Bristol City in the FA Cup and Blackpool at home a week later.
"The only way we can even hope to put this right is by stringing some good results together.
"Nobody wanted to let the match at Peterborough go like that and, believe me, the players were hurting badly afterwards.
"We have to remember we are fourth. But we have to learn the lessons from the last two matches, and we all believe we have."
