Since Vatican II said (On the Liturgy # 10) that the Mass is the renewal of the new covenant, and since the Council of Trent (DS 1743) said the Mass is the sacrifice of Calvary represented, "only the manner or offering being changed", therefore we would expect Mary to have a role in the Mass parallel to that which she had on Calvary.
Pope John Paul II in an address in St. Peter's square on Sunday Feb. 12, 1984 (from English edition of Osservatore Romano, Feb. 20, 1984, p. 10) said: "Today I wish to dwell with you on the Blessed Virgin's presence in the celebration of the Liturgy.... Every liturgical action ... is an occasion of communion ... and in a particular way with Mary.... Because the Liturgy is the action of Christ and of the Church ... [and] she is inseparable from one and the other.... Mary is present in the memorial--the liturgical action--because she was present at the saving event.... She is at every altar where the memorial of the passion and Resurrection is celebrated, because she was present, faithful with her whole being to the Father's plan, at the historic salvific occasion of Christ's death."
A sacrifice consists of the external sign and the interior dispositions which the sign expresses. In the Cenacle the external sign was the seeming separation of His body and blood. On the Cross, it was the physical separation. But in both cases, and on our altars, the interior is the disposition of His Heart, most basically, obedience to the Father (cf. Rom 5. 19 and Lumen gentium # 3). His disposition on our altars is not a repeat of that which He had on Calvary, it is the continuation, for death makes permanent the attitude of soul with which one leaves the body. Mary shares in the external sign of the Mass in that the flesh and blood are still those He received from her. She shares in the interior dispositions of His Heart, with which she is eternally united. Therefore the Mass is not the time to stop thinking of her. Rather, the more closely one is united with her, the more closely one is united with Her Son. Therefore, let no one say we should forget her at Mass. Rather, the more closely one is joined to her there, the more closely to Jesus--and vice versa.
From the file, "The Role of Our Lady in Each Mass", by Fr. William G. Most