Please accept my sincere apology on behalf of our company. I am very sorry to learn that your experience with Jane, our Customer Service Representative, was less than adequate. She should have handled the situation differently and transferred your call to someone with more authority.
Acknowledge the hurt and damage done.
I understand your frustration at having made a simple request to speak with a supervisor—someone who had the authority to fix the problem at hand. We let you down in that regard and for that, I am also