General:
* Apology: This is the most direct noun, meaning a statement of regret.
* Expression of regret: This is more formal and emphasizes the feeling of sorrow.
* Contrition: This emphasizes deep sorrow and remorse.
Specific:
* Acknowledgement of fault: This emphasizes recognizing responsibility.
* Act of remorse: This highlights the action taken to show regret.
* Plea for forgiveness: This focuses on seeking pardon.
Figurative:
* A humble offering: This suggests the apology is a gift of sorts.
* A gesture of reconciliation: This emphasizes the desire to mend a relationship.
The best noun to use depends on the specific context and the desired emphasis.