Forgetting to put an order in is probably the worse thing that can happen to someone working the front of the house of a restaurant. The few times this happened to me I just told the customer the truth. Although they weren't very happy with what happened they accepted I made a mistake, and we were able to work it out.

Recently my dad forgot to put an order in and realized it after the customer was already waiting for 20 minutes in the store. Instead of telling the customer the truth my dad tried to slyly put the ticket in without the customer noticing. My dad isn't very sly though. The customer saw what my dad did and got furious and stormed out. 5 minutes later the customer was expressing his anger on yelp with a 1 star review. Moral of the story: Just tell the truth; even if a customer won't accept your apology, at least you are owning up to your mistake--it looks better on your part