The midfielder, who played the whole game, made little impact on the match at the Aloha Stadium but squared up to Lucas following a strong second-half challenge. Brazilian striker Bare scored the only goal of the game for the Japanese side three minutes into the semi-final of the inaugural Pan Pacific Championship.
The Galaxy will face Sydney FC in the third-place play-off on Saturday after the Australian side lost 3-0 to Houston Dynamo in the second semi-final.
Beckham, who is hoping to win a place in Fabio Capello's England squad next month, was left bemoaning his side's lack of cutting edge and a sluggish start in Hawaii.
"Obviously it's always disappointing when you lose the game, when you don't start off the game well and properly, then that happens," he said.
"They capitalised on that first breakthrough, but we got back towards the end of the first half and we had a few chances.
"The second half was a lot better, we started playing football, we started playing with confidence and we created chances. But you don't get anything unless you put them away."
Galaxy coach Ruud Gullit was pleased to see Beckham get 90 minutes under his belt but felt his side were hampered by a lack of preparation having arrived in Hawaii only two days ago.
"We thought David might only play 30 minutes because we were concerned about the artificial turf but he felt good out there so we kept him on," he said.
"We had to adapt a lot to the pitch, we didn't train on the pitch at all. It took us a little bit of time to adjust."