The veteran boss had hoped the Clydesdale Bank Premier League clash with Dundee United would allow him to go out on a high ahead of his retirement, with Derek McInnes now set to take over the Pittodrie hotseat.
But a last-gasp winner from Ryan Boulding allowed United to pip both the Dons and Kilmarnock to the final top-six spot in the SPL before the league split, with Killie suffering defeat against Dundee.
Brown said: "I'm very fortunate. I've lived the dream of every football fan. I've been able to work with Aberdeen and I've had a long time in the game and I'm very grateful for that. The biggest disappointment I've had is that I've sent 3,000 or 4,000 folk up the road without what we all wanted - and that was a victory.
"The over-riding feel is disappointment for the terrific support we had. They were absolutely fantastic throughout the match and it was a major disappointment to send them up the road without the result that they craved and we craved."
Kilmarnock had been in the driving seat for the top-six berth at the start of the day but their own result meant whoever came out on top at Tannadice would book a place in the top half of the table instead.
Brown added: "When we heard that Dundee were ahead, we went for it. I'm sure we could have got a draw, sitting there and playing as we had played. But, in an attempt to try to get the winner, we took too many chances and that enabled them to get the winning goal. But they were the better team in the second half."
United boss Jackie McNamara now wants his side to use the remaining games to finish as high up the table as possible.
He said: "It was a great feeling to score when we did. We were on the end of a late goal from St Johnstone the other night and we were a bit deflated after it. This goal more than makes up for it. I think it was deserved, especially in the second half. I was just delighted for everybody connected with the club.
"We've had a couple of disappointments over the last couple of weeks and today makes up for it. Inverness are seven points ahead of us and that's the target now. Today was about winning and doing our jobs properly and we did that."