If the laity do not offer a liturgical sacrifice, they might consider the Mass an inspiration for the spiritual life:
98. In order that the oblation by which the faithful offer the divine Victim in this sacrifice to the heavenly Father may have its full effect, it is necessary that the people add something else, namely, the offering of themselves as a victim.
The biblical witness of Peter and Paul:
99. This offering in fact is not confined merely to the liturgical sacrifice. For the Prince of the Apostles wishes us, as living stones built upon Christ, the cornerstone, to be able as “a holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ.”[1 Peter 2:5] St. Paul the Apostle addresses the following words of exhortation to Christians, without distinction of time, “I beseech you therefore, . . . that you present your bodies, a living sacrifice, holy, pleasing unto God, your reasonable service.”[Rom. 12:1] But at that time especially when the faithful take part in the liturgical service with such piety and recollection that it can truly be said of them: “whose faith and devotion is known to Thee,”[Roman Missal, Canon of the Mass] it is then, with the High Priest and through Him they offer themselves as a spiritual sacrifice, that (their) faith ought to become more ready to work through charity, (their) piety more real and fervent, and (they) should consecrate (themselves) to the furthering of the divine glory, desiring to become as like as possible to Christ in His most grievous sufferings.
Not every believer is prepared today for martyrdom. And indeed, the snarky among us have suggested that the “quick” killing of martyrdom can be somewhat less arduous than the daily sacrifices needed for the care of others, for the hard and tenacious work we often do with little or no apparent effect.
At any rate, Pope Pius seems to suggest the Mass as an inspiration for the imitation of Christ. Certainly we can imitate him in profound ways, and with the assistance of grace. All too often such ways are quiet and unseen, yet persistent and no less faithful. The pope has references Romans 12:1, a more popular choice for wedding liturgy these days. Certainly, if a sense of sacrifice was extended more explicitly to sacraments such as marriage, that would be a good development, no?
Consult the full document Mediator Dei on the Vatican web site.