The winners broke the top-seeded Bryan brothers' service in the final game on their fifth match point, with Sock smashing the winning forehand on a Mike Bryan second serve.
Pospisil said they had a simple formula for beating the all-time best doubles pair in Grand Slam history.
"Close your eyes; hope you play the best tennis of your life," he said, smiling.
Sock and Pospisil were playing on Centre Court for the first time.
"We had a lot of fun, people could see that," Sock said. "That's part of why we did well. We really enjoyed being out there. As kids we grew up watching this tournament. This is what we kind of dreamed of doing."
The 21-year-old Sock became the third-youngest player to win both a Grand Slam men's doubles title and a Grand Slam mixed doubles championship in the Open era, adding to the mixed title he won with American Melanie Oudin at the U.S. Open in 2011.
Todd Woodbridge and John McEnroe, both 20, were the only men to win both titles at a younger age, with McEnroe being the youngest.
The 36-year-old Bryan brothers' Grand Slam championship slump continued.
The Americans, who have won a record 15 Grand Slam doubles titles, including three at Wimbledon, had not reached the final at any of the last three Grand Slam tournaments -- after winning four major titles in a row before that.
"Unfortunately we were on the losing end of it, which doesn't feel good," Bob Bryan said. "But we'll look back on this run we had here with good feelings. I thought we fought hard for two weeks and turned it into a final ... almost another trophy."
He said he wasn't surprised by their opponents' quick success as a team.
"That happens a lot -- the honeymoon period is sometimes tough to stop," he said. "We faced it many times. Guys playing together the first time are really excited. They have great runs."
It was the first Wimbledon men's doubles final to feature four players from North America since 1983 when Peter Fleming and McEnroe defeated fellow Americans Tim and Tom Gullikson.