A late goal from summer signing Jess Driscoll rescued a point for Posh after the hosts had taken a 2-1 lead minutes earlier a speculative long range shot.
An own goal had put Posh in front midway through the first-half. Burton equalised before the break, but four points from three Midlands Division matches represents a solid start.
Brown said: “We have shown we can comete. We’ve done just that in all of our three games so far, but there is so much more to come from us once we really come to terms with the level.
“We had players playing out of position today and the attitude from all of them was excellent. We have things to learn, but the squad has depth and we have flexibility.”
Posh were the better side in the early stages and Beratrix Borque struck a post with a snapshot, while skipper Keir Perkins caused many problems to the home defence.
The goal Posh deservd arrived when a Stacey McConville free-kick was turned past her own ‘keeper by a Burton defender, but a penalty dragged the home side level within minutes.
Burton’s greater experience at this level showed at times in the second half, although Driscoll fired a shot into the sidenetting and Ellen Marson shot too close to the goalkeeper.
The hosts went in front with 10 minutes to go, but Driscoll was on hand to save the day from close range four minutes from time following another McConville free kick.
Posh: Cooper, Copson, Steward, Borque, O’Neill, McConville, Perkins, Stevenson, Driscoll, Marson, Breakwell. Substitutes: Parrett, Dodwell.
Posh under 23s were beaten 3-1 at Cardiff City today. Recent recruit Andrew Oluwabori did bring Posh level at 1-1 early in the second half.
Posh: Blackmore, O’Connell, Powell, Barker (C), Peters, Fernandez, Poku, Bejang, Arnold, Harris, Oluwabori.
Subs: Bodie, Lakin, Spence-Adams, Gyamfi.