With 10 minutes remaining on the clock, Cammy Bell brought down Niall McGinn but, instead of pointing to the spot, Norris booked the striker for diving.
Rory Fallon had volleyed the Dons ahead after seven minutes, with Paul Heffernan levelling matters shortly before half-time.
Brown said: "I've seen it again and it's without a doubt a penalty and a red card.
"I've been told by (SFA Compliance Officer) Vincent Lunny and (SFA Head of
Referee Development) John Fleming that if you feel the referee has made a mistake then you are able to say that.
"I had asked the fourth official to speak to the referee and ask him why he didn't give a penalty and a red card to the goalkeeper but it doesn't make much difference now as it has passed.
"Because the league is so tight, the decision is disappointing, but the implications are huge.
"We can't totally lay blame on the official as we missed what I would describe as five very good scoring chances."