Gareth Evans helped to lift Pompey after coming off the bench at the start of the second half.
They were 2-1 down to 10-man Burton, who had scored twice in the opening stages through Joe Sbarra and Kieran Wallace.
John-Joe O’Toole was then sent off before Ronan Curtis reduced the hosts’ deficit just before the break.
Evans was part of an improved display following the restart, although it took a stoppage-time Brett Pitman penalty to salvage a point.
The midfielder said: “It was obviously disappointing to go two goals down so early on, but the one we got back before half-time gave us that glimmer of hope.
“The sending off meant it was pretty much one-way traffic and it was just a case of trying to get the ball in the back of the net.
"We’re all in it as a squad and you can’t let your heads drop and think it’s all over – you have to work your way back."
“But it’s difficult when your opponents have got so many men behind the ball and we’re frustrated not to have won the game.
“We’re all in it as a squad and you can’t let your heads drop and think it’s all over – you have to work your way back and we did, so that’s a positive.
“Their keeper’s had a decent night and made some good saves, but I thought there was an obvious penalty decision for a foul on Andy Cannon.
“If they had given that one then it would have been 2-2 earlier and we’d have more time to go on and score again.
“But you can’t blame the referee too much because we had plenty of chances that we couldn’t put away.”
Kenny Jackett opted to switch systems for the second half, with Evans brought on as a right-sided wing-back.
He said: “The manager felt that we could get at them in the wide areas and there was space for us, so we went to three at the back.
“He just told me to get on the ball and cross it in for the two strikers and the number 10 running in as well.”