There’s never really a great way to apologize, but there are plenty of terrible ways.
If you’re at a coffee shop, and you spill coffee on someone by accident, what do you say? You’ll likely say “Oh my god, I’m so sorry!” When you mean it you say you’re sorry – it’s a primal response. You wouldn’t say “Oh my god, I apologize for any inconvenience this may have caused!” But that’s exactly how most companies respond when they make a big mistake.
Mistakes happen. How you apologize matters. Don’t bullshit people – just say “I’m sorry”. And mean it.