If Bullseye fails his attack while carrying a light object, did he still deal the 1 penetrating damage?

ANY OBJECT A WEAPON: Bullseye can pick up and use light objects as if he had Super Strength. If he hits with an attack using an object, after the attack is resolved; deal 1 penetrating damage to his target.

"if he hits with an attack..."

The means it has to be successful, then you deal the 1 penetrating damage.

The answer to your question is in the description.

Thank you very much!