Beckham, in his first game since reaching 100 international caps for England in a friendly against France on Wednesday, played in a variety of different positions as head coach Ruud Gullit tried in vain to find a successful formation.
The former England captain and his Galaxy team mates struggled to cope with playing at altitude, just outside Denver.
"It is always going to be tough when you travel when you have got international games," Beckham told reporters. "It is always tough when you are back from England and you are adjusting to the time difference.
"I felt ok for most of the match but I was maybe not at my sharpest and maybe the altitude had something to do with that."
Former Manchester United winger Terry Cooke opened scoring for Colorado after 10 minutes.
The Galaxy went further behind after an hour when defender Abel Xavier was adjudged to have fouled Rapids forward Omar Cummings inside the penalty area. Christian Gomez converted the spot-kick after furious protestations for the visiting players.
"I find it hard not to criticise some of the decisions tonight but I've been told I'll be fined if I do," said Beckham. "But certain decisions change games. I think that has happened tonight."
Cummings added Colorado's third goal on 67 minutes before Colin Clark scored the fourth with 10 minutes left.
Xavier was sent off late in the game for using abusive language towards referee Abiodun Okulaja and Colorado substitute Ciaran O'Brien was also dismissed after a foul on Carlos Ruiz.