Sadly, this pious act is not taught these days, and is not specifically mentioned within the General Instructions of the Roman Missal. However, there is nothing wrong with personal acts of piety and reverence. After all, “lex orandi, lex credendi” (loosely translated as, “how we pray shows what we believe”). During the consecration, we truly are at the foot of the cross 2,000 years ago, where Jesus is sacrificing Himself for our sins, and we should act accordingly.
When the priest raises the host and then the cup, at each of those times my family and I bow our heads (while remaining kneeling, of course) and strike our left breast 3 times while quietly saying, “Through my fault, through my fault, through my most grievous fault”. Then we say something like, “My Lord and my God, be merciful on me, a sinner”.
We also bow our heads (while kneeling) at the point of the Mass when we pray, “Lord, I am not worthy to receive you, but only say the word and I shall be healed”, and then while keeping our heads bowed, we say additional prayers, like The Act of Contrition, in order to prepare us to receive Him.
I remember my grandparents doing these pious acts back when the Novus Ordo Mass first came out. They wished to retain some of the reverence from the Old Latin Mass (now the Extraordinary form of the Mass). My family and I now carry on what my grandparents taught me, and hopefully, my children will teach their children (unless some of them are called to the priesthood Then they can teach their spiritual children).