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The newly-appointed gaffer kept his players behind in the dressing room after they first conceded a late equaliser from Seagulls striker Jake Robinson they missed three penalties in the following shoot-out.
And with star striker Ben May seemingly unwilling to take one of The Lions' five spot kicks, Donachie hit out at the attitude of his players and their failure to kill off Brighton in normal time.
"I am very, very disappointed - the most I have been in my career," said Donachie after the game. "I have had lots of lows and highs but I am disappointed because of the performance.
"We all have to take responsibility - the team I picked and the way we played - and I have told the lads this.
"I am trying to take the positives. Normally I would rather lose that kind of game than most others - but not in the way we lost it."
Millwall had taken a first half lead through captain Paul Robinson after Guy Butters was sent off for the visitors but they were left to rue their failure to take advantage of their dominance in the second half when Brighton pounced at the death.