The "Texans" didn't win the Battle of the Alamo. General Santa Anna and his army did. When the Alamo was lost the battle cry "Remember the Alamo" was started and it mobilized the Texans to resist Santa Anna even more until Texas was eventually in American hands.
The Alamo started by Mexico encouraged foreign settlement in Texas, but the Mexicans far out numbered the Texans. The Texans wanted to be independent, so the Texans started a Texas Revolution, and the Alamo was the very first battle to happen in the Texas Revolution.