+1 to Parody.
Core Set Rulebook, p.12 wrote:
Suffer Damage, If Necessary. If you fail a check to defeat a monster, you suffer an amount of damage equal to the difference between the difficulty and the result. Unless the card specifies otherwise, this damage is Combat damage.
Even when a Monster's Check to Defeat is a non-combat check, you suffer Combat damage if you roll less then the check's difficulty.
Note, however - this is only for banes with the type "Monster". You do not automatically suffer damage when you fail to defeat a Barrier - each Barrier tells you exactly what are the consequences of failure.