"The hamstring, I tore on Tuesday and I had a little bit of a cold Wednesday morning - which I actually did, funny enough," Beckham said in the postgame press conference.
"The hamstring was something I was disappointed about because I think we'd had three tough games in nine days and I felt great on that Tuesday, [but] pulled up short on Tuesday with the hamstring."
But Beckham said taking out the title - his eighth senior premiership in his career - makes all the pain worth it in the end.
"Being successful always feels good," Beckham added. "Proving people wrong feels even [better].
"I think people doubted us. We're the Galaxy, we're the biggest club in this country and this league, and we're proud tonight, we're proud to be a part of this."