The pair won gold in Beijing four years ago and looked set to repeat the feat as they went into the medal race of the Star regatta in Weymouth in first place.
However, an eighth-place finish in the medal race - worth double points - meant they were overtaken by Sweden, whose pairing of Fredrik Loof and Max Salminen won the race and title.
Team GB finished on 34 points, two behind Sweden, with Brazil on 40 points at the end of the regatta.
Simpson said: "You are never 100% confident. We didn't get it right and can't blame anyone but ourselves. We had a great regatta overall.
"We are really frustrated. We tried our hardest, but it wasn't to be."
Awarded the MBE in 2009, Simpson was featured in our official matchday programme as one of our Spurs Olympians last season.
He told us then that his sporting passions - sailing and football - were both born in North London. He attended his first game here at White Hart Lane 'against QPR sometime in the late 1980s/early 1990s', while he laid eyes on a yacht for the first time at a boat show at nearby Alexandra Palace.