The Dons' record of failing to find the net against Hearts was extended to eight matches, the last coming in January 2010, as they lost 2-0 at Tynecastle.
Ryan Stevenson and Calum Paterson scored for Hearts while Aberdeen faltered in front of goal with young substitutes Jamie Masson and Declan McManus both missing chances.
Brown, whose first match in charge of the Dons was a 5-0 defeat at Tynecastle two years ago, described the decision to award Hearts a penalty, which was converted by Stevenson, was "soft".
But he was more concerned with his side's failings and their on-going draught against Hearts.
"It's just one of those things," he said. "We inherited a situation where Hearts were beating Aberdeen and we've not managed to redress that.
"The two young lads are distraught. I could have run from the dugout and scored."