The first Mass

The Last Supper was the first Mass, it did not duplicate His redeeming sacrifice on the Cross, although it looked forward to it and expressed His intention in performing it.

Augustine
"Christ was carried in his own hands when, referring to his own body, he said, ‘This is my body’ [Matt. 26:26]. For he carried that body in his hands" (Explanations of the Psalms 33:1:10 [A.D. 405]).

Aphraahat the Persian Sage
”After having spoken thus [at the Last Supper], the Lord rose up from the place where he ha made the Passover and had given his body as food and his blood as drink, and he went with his disciples to the place where he was to be arrested. But he ate of his own body and drank of his own blood, while he was pondering on the dead. With his own hands the Lord presented his own body to be eaten, and before he was crucified he gave his own blood as drink”. (Treatises 12:6[A.S. 340]).

As a Sacrifice

*Because it is the memorial of Christ’s Passover, the Eucharist is also a sacrifice; the sacrificial character of the Eucharist is manifested in the very words of institution: ‘This is My body which is given for you’ and ‘This cup which is poured out for you is the New Covenant in My blood. (Luke 22:19-20). In the Eucharist Christ gives us the very body which He gave up for us on the cross, the very blood which He ‘poured out for many for the forgiveness of sins.’ (Matthew 26:28). The Eucharist is thus a sacrifice because it is a memorial and because it applies its fruit. Every Mass makes the one and only sacrifice of Calvary mystically present to those who participate, so it is not a new sacrifice but the very same one, not repeated but embodied in another time and place, so as to be accessible to all God’s children.

Council of Ephesus
"We will necessarily add this also. Proclaiming the death, according to the flesh, of the only-begotten Son of God, that is Jesus Christ, confessing his resurrection from the dead, and his ascension into heaven, we offer the unbloody sacrifice in the churches, and so go on to the mystical thanksgivings, and are sanctified, having received his holy flesh and the precious blood of Christ the Saviour of us all. And not as common flesh do we receive it; God forbid: nor as of a man sanctified and associated with the Word according to the unity of worth, or as having a divine indwelling, but as truly the life-giving and very flesh of the Word himself. For he is the life according to his nature as God, and when he became united to his flesh, he made it also to be life-giving" (Session 1, Letter of Cyril to Nestorius [A.D. 431]).

Pope Clement I
"Our sin will not be small if we eject from the episcopate those who blamelessly and holily have offered its sacrifices. Blessed are those presbyters who have already finished their course, and who have obtained a fruitful and perfect release" (Letter to the Corinthians 44:4–5 [A.D. 80]).
  
Justin Martyr
"God speaks by the mouth of Malachi, one of the twelve [minor prophets], as I said before, about the sacrifices at that time presented by you: ‘I have no pleasure in you, says the Lord, and I will not accept your sacrifices at your hands; for from the rising of the sun to the going down of the same, my name has been glorified among the Gentiles, and in every place incense is offered to my name, and a pure offering, for my name is great among the Gentiles . . . [Mal. 1:10–11]. He then speaks of those Gentiles, namely us [Christians] who in every place offer sacrifices to him, that is, the bread of the Eucharist and also the cup of the Eucharist" (Dialogue with Trypho the Jew 41 [A.D. 155]).