3/4 creature versus a 3/3 creature, why would the 3/4 creature die?
Damage does not modify toughness, so your creature will not become 3/1. It will remain a 3/4, but it will be marked with three damage. (Some video game versions of Magic show this as 3/1, but that is inaccurate.) That alone is not enough to kill it, so something is missing from your description. 


Maybe your creature was marked with damage earlier in the turn.
Maybe an effect enhancing your creature's toughness was removed.
Maybe the attacking creature had deathtouch.
etc


A more detailed description of the scenario would allow us to give a more detailed answer.