Beckham scored his penalty but Galaxy captain Landon Donovan was among those to miss as Salt Lake won the shootout 5-4 to capture a surprise victory just four years after entering the league.
Galaxy took the lead four minutes before the break through Mike Magee, who turned in a low cross from Donovan after good work from Beckham, but Salt Lake equalised in the 64th minute when Robbie Findley blasted in from close range.
After a scoreless extra-time, the shootout went into sudden-death and the Galaxy's Edson Buddle had his shot saved by Salt Lake keeper Nick Rimando before Robbie Russell slotted home to secure the championship.
"Its always tough losing, whether it be penalties or normal play but of course we can be proud of where we have come to," said Beckham, whose team reached the championship final a year after having one of the worst records in the league.
Salt Lake were crowned champions, in front of a 46,000 crowd at Seattle Sounders' Qwest Field, despite having lost more games than they won in the regular season.
"They deserved to be here and they deserved to win tonight in the end," the midfielder told reporters.
"There are probably very few players that are 100 percent, this time of the year. No, he was obviously a little bit hobbled, certainly wasn't 100 percent," he said.
The England midfielder was involved an early incident when his challenge on Salt Lake's Argentine playmaker Javier Morales left the player needing to be substituted.
"We deserved to win the game... we are the best team in this league," he told reporters.
Arena agreed that the result was a fair one, saying: "We didn't play well enough over the 120 minutes to win the game."
