It seems like we ask for forgiveness both at Mass and in other standard prayers. Can any sins be forgiven without the Sacrament?
The Sacrament of Reconciliation (Penance) is generally required for the remission of mortal sins committed after Baptism (which forgives all sins). The Catechism of the Catholic Church (CCC) explains, “Christ instituted the sacrament of Penance for all sinful members of his Church: above all for those who, since Baptism, have fallen into grave sin, and have thus lost their baptismal grace and wounded ecclesial communion. It is to them that the sacrament of Penance offers a new possibility to convert and to recover the grace of justification” (CCC 1446).
While sacramental confession of all sins is recommended (cf. Code of Canon Law, 988.2), venial sins may be confessed directly to God. Moreover, the Catechism notes, “[Scripture and the Fathers] cite as means of obtaining forgiveness of sins: efforts at reconciliation with one’s neighbor, tears of repentance, concern for the salvation of one’s neighbor, the intercession of the saints, and the practice of charity which covers a multitude of sins” (CCC 1434).
Perfect contrition also obtains forgiveness. “When it arises from a love by which God is loved above all else, contrition is called “perfect” (contrition of charity). Such contrition remits venial sins; it also obtains forgiveness of mortal sins if it includes the firm resolution to have recourse to sacramental confession as soon as possible” (CCC 1452).