A deflected shot put the Stags on the way to a defeat, despite their first ever goal against the new League Two leaders.
Afterwards manager Paul Cox bemoaned his side’s inability to make the most of half-chances in front of goal.
He said: “You can say they were lucky but I want myself and the players to start being lucky too. I want my players to shoot and try to affect the game in the last third. You would be amazed at what happens if you hit the target.
“I thought we were the better side without actually giving too much of a threat in the last third. Their first goal came massively against the run of play and we were up against a strong wind too.
“We have got to be a bit better in both boxes and we are perhaps missing one or two ingredients to polish off all the hard work we are putting in.
“We are short of a fox in the box to get on the end of Matt Rhead’s flicks – a bit of X-factor – but we know they don’t grow on trees.
“There are no excuses. We were up against one of the best teams in the division.
“Burton will be in the top three at the end of the year, so if we take them a benchmark we are not far away in certain areas.”
Sam Clucas, restored to the starting line-up after a failed bid by Chesterfield for the wingman, Lee Beevers and the industrious Ollie Palmer all had good first half shooting opportunities as the Stags started brightly in a low-key opening.
The game turned on a moment of fortune for Burton just before half-time when Alex Macdonald’s hopeful 20-yard drive was deflected twice to beat Dimitar Evtimov, the Forest loan keeper who made a surprise debut.
The Stags again dominated possession at the start of the second-half, before a Burton breakaway ended with another fortunate break. This time Martin Riley’s tackle fell kindly for Callum McFadzean to slide in from the edge of the area.
Matt Rhead headed in from Adam Murray’s ball into the area to set up a tense finish, the Stags’ first ever goal against Burton.
But despite a red card for Robbie Weir in the closing stages after he squared up to Mansfield’s Jamie McGuire following an off-the-ball incident, Burton hung on.