The hosts, who grabbed a goal through Mark Stewart, were punished by Dons striker Niall McGinn, whose second-half hat-trick left them nine points adrift at the foot of the SPL table.
Brown said: "We were excellent.
"Niall got a hat-trick but it wasn't just him.
"We were far more like ourselves and got what we deserved.
"It's a great three points and will get the confidence right back up again."
Aberdeen got the second half off to a whirlwind start by taking the lead in the 46th minute. McGinn slid in to break the deadlock with a close-range tap-in from Cameron Smith's cross which eluded the Dundee defence.
In-form McGinn made it 2-0 after 68 minutes. Johnny Hayes caused havoc with a whipped cross for McGinn, who was all alone to nod past the helpless Rab Douglas and seal the three points.
Stewart pulled a goal back in the 82nd minute with a low drive after Colin Nish had flicked on Gary Irvine's long throw-in.
But McGinn made the game safe when he knocked home the rebound after Douglas had parried Hayes' shot.