Mary's whole reason for being (besides, you know, saying yes to God and birthing the savior) is to bring us closer to her son, so the fact that people around the world gather to encounter the physical presence of Jesus provides some fulfillment to her mission. We also know that, like the rest of the saints, Mary is present with us in the mass:
And so we join the angels and the saints in proclaiming your glory as we sing
(I love the Latin! ...and the fact that I have a fair understanding of a language I've never been taught. I can't imagine how much more I would know if I grew up attending mass completely in Latin as in pre-Vatican II!)
What makes Mary unique in the context of the Eucharist is that she was the original tabernacle. We make our receptacles out of precious metal today to show respect for the contents, following God's example: He chose Mary, a woman without sin, to be the perfect vessel that would carry so sacred a body.
In the mass and in the Eucharist, we become like Mary. We are forgiven our venial sins at the beginning of mass and present ourselves as-perfect-as-possible to receive Jesus, body and soul, into our own bodies. Our "amen" echos Mary's "yes" and her total surrender to God's will. If we approach to receive Communion without truly repenting of our sins or without upholding the tenants of the Church God has given us, we disrespect Christ by putting Him in a tainted vessel. No one (save Mary) is spotless, but it is through adherence to Truth and confession of wrong that we become worthy enough to enjoy a physical intimacy with Jesus. Mary carried Jesus inside her for nine months - what joy that must have been. The Eucharist is the closest we can get to her experience.
After receiving the Eucharist and returning to my pew to give thanks for this "communion" with Jesus (because that's what it's called!), I think of Mary. I imagine a veil over my head and bask in the same peace she carried throughout her life. Just for a moment, I feel a deep connection to Mary, as I've become like her - a vessel for Christ.
Give it a try.