I’ve never once heard the act of contrition within the context of the Mass. Are you sure you mean the “O my God, I am heartily sorry for having offended Thee…”?
Maybe you’re thinking of the Confiteor…“I confess to Almighty God…”
The Confiteor is optional in the Novus Ordo, I believe; the celebrant can use only the Kyrie if he chooses. And in the TLM its always prayed.