The Bavarians appeared to be on their way to European glory at the Allianz Arena when Thomas Muller headed them into the lead in the closing stages of the game.
However, Didier Drogba restored parity within minutes of the opener, before Chelsea eventually proved to be the stronger of the two from 12 yards - much to the shock of the Germany international.
"We are all very disappointed, down in the dumps. What can I say? We lost, but were clearly the better team," Boateng was quoted as saying on the official Uefa website.
"I just can't believe it. A dream broke down within seconds. We always had the advantage.
"We were leading 1-0, had a penalty [which Arjen Robben missed] and were leading in the penalty shootout. But that's how football can be."
Bayern take on Netherlands in a friendly on May 22 in their last game of the 2011-12 campaign.