The Galaxy were beaten 1-0 by Costa Rican outfit LD Alajuelense in Alajuela courtesy of captain Pablo Gabas' brilliant free-kick just prior to the half-hour mark.
After the loss - the Galaxy's second in a row in the competition - Beckham said that the opposition were just more impressive on the night.
"Their goal was a great goal," Beckham said.
"Sometimes you have to hold your hands up and say you were beaten by a team that performed better on the night and scored a great goal."
And Galaxy skipper Landon Donovan felt that the artificial surface at the Estadio Alejandro Morera Soto did play some part in the defeat.
"This field is tough," Donovan said. "You've got to give them credit because they know how to play on this field and we were a little naïve in the way we played."