With 10 minutes remaining in the match Cammy Bell brought down Niall McGinn with a sliding challenge, however referee Euan Norris instead booked the striker for diving.
Rory Fallon's brilliant volley gave the Pittodrie side the lead they deserved before Paul Heffernan got Kilmarnock back on terms five minutes before half-time. Aberdeen wasted several good chances and were unable to grab a vital second goal.
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.
"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."
Killie boss Kenny Shiels had a contrasting view on the balance of the game to his opposite number and also expressed his delight at signing Kris Boyd on a deal until the end of the season.
"The signing had an effect as (Paul) Heffernan and (Jamie) Langfield were outstanding," said Shiels. "He's made a major contribution to this club and is a legend here - it's great to have a player like that here.
"Aberdeen have quality right through their team, I think after they enjoyed the better of the first 20 minutes and hit the post, that could have killed it off. But we dug in, made some chances and then got the goal we deserved. The first 20 minutes of the second half we were bossing it and then Aberdeen started hitting us on the break."
- Sports & Recreation
- Paul Heffernan
- Cammy Bell