It is necessary to have an empty crate slot before you enter the battle in order to receive a crate after battle. If you do not have any empty crate slots, open at least one crate to free up a slot and start receiving crates again.

There are also a few criteria you must meet in order to be eligible for crates:
  1. Finish in first, second or third in Free for All battles.
  2. Be in the winning team in Team Deathmatch or Conquest modes.
You can find more information on the "i" icon right above the 'Battle button.