There seems to be undue sense that the Mass is about the Last Supper, and that is what is about primarily, well any Catholic should be aware that the Mass is the re-presentation -emphasis or "re"- of the Sacrifice of Calvary, in an unbloody manner. Yes it is that, but it is more than that, it is also the Worship of Heaven itself.
Calvary is important, not because of Christ's suffering, but because of Christ's total self giving. Killing and blood in "sacrifice" is incidental, the important thing is the offering. On the Cross we glimpse in this brief three hour period the Eternal offering of the Son to the Father. At the heart of the Trinity itself is this act of total self offering. This is the nature of Heavenly Worship: participation in this Eternal Sacrifice, this is the sacrifice which will be offered in "Spirit and in Truth" that Jesus refers to when he speaks to the Samaritan woman at the well. This is why God can say, "I do not want your sacrifices, but a humble and contrite heart, this is what is acceptable to the Lord". It is the humble and contrite heart that the Lord himself offers, as an act of total self-giving.
Andre Rublev shows this in the "Old Testament Trinity", the Son - in blue and brown, points to the offering of the lamb, as he looks in love to the Father clothed in robes of light. The Holy Spirit looks to us the viewer and invites us into his embrace so that we can enter into this circle of Heavenly Worship by entering ourselves into the Sacrifice of the Lamb.
In order to rediscover the true meaning of Christian worship, I think it is absolutely imperative to re-orientate our worship.