No, we cannot apply a discount code to an order that has already been placed. If you have already ordered, message us here with your order number and the code, and a colleague will get back to you on this.
Most codes stay valid for a while, so check the expiry date on yours; you can use it on a future order.
Discount codes do not apply to items that are already on sale, and the welcome code does not apply to sale items or bundles, so if your order was a sale item or a bundle the code would not have worked at checkout either. There is more on that in Why is my promo code not working?.