Beckham came on as a 68th minute substitute, making his first appearance since suffering a knee injury on August 29.
The draw leaves LA needing to win their final regular season game -- away to the Chicago Fire on Sunday -- to have any chance of making the play-offs.
Galaxy took the lead in the 15th minute when Troy Roberts headed in a Landon Donovan cross at the back post.
New York, already assured a play-off spot, drew level within a minute though as Jozy Altidore thundered home a header after a superb cross from Dave van den Bergh.
Beckham, who is not yet fully fit, received a warm welcome from the home supporters when he entered after the break but made little impact on the game.
Photograph: Getty Images | Text: Reuters