Dons striker Scott Vernon had a penalty saved after Gary Deegan scored what proved to be the only goal early in the second half.
"We deserved to win the game," said Brown." We were the better team, the statistics will confirm that.
"It's a desperately disappointing afternoon."
Brown was frustrated by his team's finishing at Easter Road.
"Hibs had two shots on target in the entire match and one went in over the goalkeeper's head, the other one was saved," he told BBC Scotland.
"When you find a home team with two shots and we've bombarded them in the last 20 minutes of the game, missed three great chances and a penalty kick, you can only say that we're desperately unlucky.
"Our finishing was a bit slack but the chances were created, the determination was there. I can't fault any player for lack of effort. We showed a real appetite to get back in the game when we went a goal behind."
The Pittodrie boss will now turn his attention to the remainder of Aberdeen's Scottish Premier League campaign.
"I still think there's potential to get the third place," added Brown. "Our objective now is to get right into that top group."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.