A poor touch from Isaac Osbourne set up Gregory Tade for the opener and, although Niall McGinn levelled, Rowan Vine scored after Jamie Langfield failed to collect a corner, with two Aberdeen players unable to head to safety.
Callum Davidson then capitalised on some hesitancy before Steven MacLean cut back for Dave Mackay to net.
Brown said: "It was a poor performance. How we can go from being excellent at the weekend to playing poorly in the last period of the game was unaccountable.
"Each goal was a gift. The first goal we conceded was alarmingly softly but St Johnstone took their chances."
Meanwhile, Brown confirmed Aberdeen were hoping to sign Czech goalkeeper Dan Twardzik.