Burnley got off to the best possible start with Charlie Austin scoring within a minute of the kick off and Ferguson said: "We got caught cold and it took us another 20 to 25 minutes to even get into the game.
"You can't start any game that sloppily and expect to win games. In another season drawing at home to a side in the top eight after losing a goal in the first couple of minutes might be seen as a good point, but in the position we are in it's not a good result.
"Because we lost the first seven games of the season we now have to win virtually every other game to have a chance of staying up. That's why this was a vital match and when we did turn it around and take the lead I really felt we would go on and win.
"The substitutions worked well for us and I was pleased with the effort and attitude of the players in the second half. They had a real go and our energy levels were what they should have been at the start.
"We couldn't see the game out though and that was disappointing. Our concentration levels at the end of the match were poor again and that's one of the main reasons why we are bottom of the table."
The point took the Clarets a place up the table and one point closer to the play offs because of Middlesbrough's heavy defeat at Ipswich. Dyche said: "Factually it’s a point gained after Middlesbrough lost today, but it is frustrating after a good first half on what was an awkward pitch to play on.
“At half time we were in good shape, but after talking to the players about the endeavour Peterborough have at home, they showed that and we just didn’t deal with it as well as I’d hoped.
“We knew there was going to be a reaction and I’m disappointed we didn’t control the game. It was difficult on that pitch, but the one thing I am really pleased about is from a really difficult spell in that second half we came through it, carried on going strong and got an equaliser.
“In the end, but for a fantastic save, we would have taken all three points, so it’s a mixture of emotions.”
He added: “The thing we have to improve on is that killer instinct. There are other factors because there are eleven others out there trying to stop you, but the next level is to ask the players to manage a game all the way through.
“As ever, I’m greedy for more because we all want to be up there. We talk about winning all the time here and the invaluable quality today is that we kept on going. We’d had a really tough 25 minutes, where we just weren’t at it, but we kept pressing and I am ever so pleased for Martin.
“When I sent him on, I asked him to sniff out a goal and he did that and he might even have nicked himself a brace. I’m pleased too for Charlie and his energy levels will grow. He has been out for a month and he found it tough as the game went on. But it’s a fantastic finish. We know he can put the ball in the net and I am delighted he’s back.”