Substitute Gary Glen netted the only goal of the game with nine minutes remaining at Pittodrie.
Brown said: "I'm desperately disappointed for the Aberdeen people.
"The fans deserve better than they got and I can understand their massive disappointment because I share it.
"It could have gone either way. I'm not saying we were unfortunate, because I'm not saying we should have won the game, but I would like to be biased and say that we didn't deserve to lose it.
"Unlike other home defeats where I felt we were unfortunate, I don't think we were tonight. Ross County took the chance they had, but the game had 'draw' written all over it.
"I thought in the first half we probably had the edge, and after the break I thought Peter Pawlett gave us an extra edge.
"We handled their main threat (Ivan Sproule) exceptionally well, so much so that he was substituted, and I thought Clark Robertson was absolutely outstanding."