David Beckham -- Flashes Injured Hand After Motorcycle Accident

David Beckham didn't walk away clean from that motorcycle accident after all -- we just saw him at LAX with his hand in a cast.

Becks held up his damaged right mitt as he walked into the terminal with his kids, and photogs asked how he was feeling after laying down his bike on Sunset Boulevard yesterday.

We broke the story ... Beckham was leaving a tattoo parlor when he swerved to avoid paparazzi, according to our Becks sources -- which explains why he didn't feel like saying much to paps about his cast.