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]
(..) Why am I here Christian? You're here because I'm incapable of leaving you alone. Then don't. - Why'd you send me those books? - I thought I owed you an apology. - For what? - For letting you believe that I... Listen to me. I don't do romance. My tastes are very - singular. You wouldn't understand. (..)2015 Fifty Shades of Grey