Niall McGinn's excellent 17th goal of the season was enough for Aberdeen, who made heavy work of their win on a pitch showing the scars of a hard winter.
They even had to play for the last 15 minutes with only 10 men, with Isaac Osbourne going off injured after Brown had made his third substitution.
The former Scotland boss felt the result possibly made up for matches the Dons should have won but could only draw.
He claimed his side could have had a first-half penalty which might have made the game more comfortable and said: "The second half from our point of view was poor; the first half was good.
"I thought we played well and there was a clear handling offence on Scott Vernon's shot which would hopefully have given us a more comfortable lead.
"The performance wasn't good in the second half and it kind of makes up for a fortnight ago against Hibs. We dominated that game and only got one point whereas in the second half here Dundee dominated and we got three points, so it perhaps evens it out a bit."