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]
(..) Just breathe. I can't go back, can I? No. But if you could ... ... would you really want to? I owe you an apology. We have a rule. We never free a mind once it's reached a certain age. It's dangerous. The mind has trouble letting go. (..)1999 The Matrix