Wisdom Behind Istighfaar After The Salah [i.e. After Tasleem]….
The wisdom behind [الاستغفار –(i.e. saying: أستغفر الله three times)] after Salah is to manifest the soul’s wrong doing – that the slave (i.e. the performer of the prayer) did not fulfill the rights of the prayer, and that he did not perform it completely and perfectly in the manner it is obligated; for it has to be the case that he did fall into some deficiency, shortcoming and negligence; so he seeks forgiveness in the hope that his shortcoming is relinquished and so that his Istighfaar (i.e. seeking forgiveness) can be a means of remedying the deficiency or shortcoming in his prayer.
[Paraphrased. Source: Fiqhul Ad’iyah Wal Adhkaar’ page 171′ parts 3&4 by Sh Abdur Razzaaq Al-Badr]