No — we cannot apply a discount code to an order that has already been placed. That is an easy thing to miss, and there may still be something we can do.
What you can do depends on where the order is:
Not yet shipped: message us here, or email [email protected], with your order number and the code. If it has not gone out, we may be able to cancel the order so you can place it again with the code applied.
Already shipped: the price cannot be adjusted after dispatch. Most codes stay valid for a while, so check the expiry date on yours and use it on your next order.
One thing worth knowing either way: discount codes do not apply to items that are already on sale, so if your order was a sale item the code would not have worked at checkout either. There is more on that in Why is my promo code not working?.