halacha - Do you do a Tashlumin (make-up) on a Shemoneh 'Esreh if you later realize that you forgot a critical insert?

If you forgot to add a critical insert in the 'Amidah (one of the special additions to Shemoneh 'Esreh at certain times of the year, eg., HaMelech HaKadosh, Ya'aleh VeYavo, etc.), and you realize at the next service that you definitely forgot to say it earlier (eg., you got the date wrong and someone pointed it out to you, or you forgot the next time also but you heard the Sha"Tz say it), do you need to make up for it (Tashlumin, perhaps because it is as if your earlier prayer did not happen), or is Tashlumin not warranted (perhaps because it was a flawed, but fulfilled, prayer)?