Furious fans vented their anger and fury at both Parkinson and the players - booed off at half-time and full-time - as they slipped to their first home defeat of the season.
Sunderland took the lead through an Aiden McGeady penalty but were quickly pegged back, conceding less than a minute later to a Ryan Edwards header.
And it went from bad to worse to after the break, Liam Boyce sealing the win for Nigel Clough’s Brewers.
There was a chorus of boos at full-time with fuming Sunderland fans showing their displeasure at both the dugout and the players as they made their way off.
Parkinson said: “I felt first half we did okay and got a great start, but to concede after the goal was so disappointing.
“We were soft in defending the throw in, switched off to the save and didn’t react.
“Concentration levels, the details, staying with people in and around the box cost us.
“We started the second half well and the crowd were terrific.
“On Saturday we conceded and responded well, kept going and got a reward, this time we conceded and stopped playing.
“Didn’t show enough conviction or character and deservedly got booed off at the end.”
Sunderland don’t have a game for another ten days after they were knocked out of the FA Cup last week at Gillingham.