It doesn’t matter how professionally perfect you are, there might come times when you commit some mistakes and you have to own up to them. Accepting your mistakes and apologising to the affected is a part of business ethics and professionalism. You should be able to write an apology email to a company, either as a customer or as a supplier, if you have committed a mistake.
Start your email by addressing the offended company with a proper greeting. Begin your first paragraph with an immediate apology and address to the core issue right away.
Take the responsibility of the mistake being committed in the following paragraph and explain the causes of the error on your part. Never try to shift blame on the offended party.
In the next paragraph, you should offer any reparations which might help ease out the offended company.
Conclude your email by repeating your apology and expressing hopes of healthier business relations in the future.