All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The prostration in Surat (Sad) isn`t a prostration of recitation (prostration required when reading certain verses of the Qur`aan), and the prayer of one who performs it deliberately is invalidated according to the Shafie school of thought. However, if he offered it forgetfully, then his prayer is valid and he should perform the prostration of forgetfulness, but if he didn`t offer the latter then his prayer is valid as well, because the latter is not obligatory. On their part, Hanafie and Maliki jurists are of the view that performing the prostration in Surat (Sad) doesn`t invalidate prayer because it is related to the recitation.
"The prostration in Surat (Sad): "…..fell down, bowing (in prostration), and turned (to God in repentance)" isn`t amongst the prostrations of recitation since Ibn Abbas narrated:"I saw the Messenger of Allah prostrating for (Surat) Sad." Ibn Abbas said: "It is not one of the resolute prostrations." {Related by Bukhari}……………………………. Rather, it is a prostration of thankfulness because Allah, The Almighty, accepted the repentance of Prophet David(PBUH), and it is recommended to offer it outside prayer following the Sharia evidence in this regard. However, it is forbidden to offer it during prayer and renders it invalid when offered knowingly and deliberately, according to the most correct opinion of the Shafie jurists. However, offering it out of ignorance or forgetfulness doesn`t render prayer invalid, but such a person should offer the prostration of forgetfulness because he`s excused." {Moghni Al-Mohtajj}.
In conclusion, your {Questioner`s} prayer is valid but try not to do this prostration {Prostration in Surat (Sad)} -during prayer-in the future so as to be on the safe side. However, it is recommended to do this prostration-outside prayer-as one of thankfulness. And Allah knows best.