The veteran boss had hoped the Clydesdale Bank Premier League clash 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."
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.
"But, in an attempt to try to get the winner, we took too many chances and that enabled them to get the winning goal."