After Charlie Austin had silenced home fans with a first-minute opener, Posh fought back in the second half and appeared to be heading for victory once Tommy Rowe's double had sent them into the lead.
But with five minutes to go, Clarets substitute Martin Paterson converted Chris McCann's accurate cross to deny Ferguson's rock-bottom Posh side.
He said afterwards: "Under some circumstances a draw against Burnley would be viewed as a decent result, but we've put ourselves in a position where we have to win games so we can't be happy with a point.
"The lads gave me a great reaction in the second half as we got ourselves ahead and I fancied us to see it out, but it wasn't to be.
"We certainly won't lack for commitment or character, but we do have to cut out the basic errors which have been costing us points all season. We cannot keep going home on a Saturday night saying 'we should have won'.
"We have been guilty of far too many lapses of concentration this season and that is the reason why we are bottom of the table."