He 'offered no apology for' his bad behavior. [=he didn't say he was sorry for acting badly]
The company issued/delivered an official 'apology' to its customers for its error.
He's a poor/sad 'apology for' a father. [=he's a bad father]
(..) you can't outrun, kid. You're pretty generous... for a thief. - I thought they killed you. - Not yet. - If you're expecting an apology... - It wouldn't suit you. I need your help. - And why would I help you? - For this. Clean slate. You'd trust me with that? (..)2012 The Dark Knight Rises