The second-seeded Bryans, the 2006 champions at the All England Club, lost to the seventh-seeded pairing of Norman and Moodie 7-6 (4), 7-6 (5), 6-7 (3), 7-5.
The Bryans, of Wesley Chapel, Fla., were bidding for their ninth Grand Slam title; they won No. 8 at the Australian Open in January. They were the runners-up at Wimbledon last year.
"It's a tough defeat, you know. You always look forward to Wimbledon every year, and everyone tries to peak here," Mike Bryan said.
"Unfortunately, we ran up against a couple of big servers, and it really kind of limits what you can do," he added. "The points are really short and that court is playing really quick and the guys were serving well. We felt like we couldn't really use our skill against them."
The brothers are still seeking their record 62nd title as a team. They tied the Open era mark of 61 men's doubles titles — set by the retired Australian pair of Todd Woodbridge and Mark Woodforde — by winning at Madrid in May.
"Every week's a new opportunity. We're not that disappointed," Bob Bryan said. "Obviously, it would have been good to get it here, but we're happy that we're tied with it. And if we don't win another title, at least we're tied with the Woodies."