How about "as a gesture of goodwill"?

You can also omit any phrase that suggests groveling, and say something as straightforward as:

We value our customers. Your experience doesn't reflect our standards. Please accept xyz as a gift. We look forward to abc in the future.

How about "as a gesture of goodwill"?

Alternatively (spinning out a broader context) something as straightforward as:

We value our customers. The experience you had doesn't reflect our standards, and we're truly sorry. Please accept xyz as a gift. We look forward to abc in the future.