Quite simply, the last supper "sends us" the Eucharist. This is the Sacrament that Roman Catholics celebrate daily (and by obligation on Sundays), the sacrament that transforms simple bread and wine into the Body and Blood of Christ. We see this instituted in each of the four Gospels, but here is the reference from Luke 22:19 for you:
And he took bread, gave thanks and broke it, and gave it to them, saying, "This is my body given for you; do this in remembrance of me."
In regards to the "message" you speak of, in addition to the message of the miracle of Jesus' body and blood, Christ also gives us a direct message to continue celebrating the Eucharist in the confines of the Mass "in remembrance of" Him. He does this by giving us a direct command in saying "do this."
Roman Catholics (like me) absolutely love Luke 22:19. : )
If there is a message in the Last Supper, it might reside in the realm of remembering the presence of Jesus. The notion of the Last Supper involves assembling Jesus' followers and commemorating his life and the legacy he will leave behind. The idea of the Eucharist and taking the blood and body of Christ comes from the Last Supper. If we were to extrapolate the meaning of the moment of the Last Supper, it represents the last time that there is unity and cohesiveness in the community of Jesus' followers. In this message, one can take away the idea that in praising the legacy and presence of Jesus, all divisions are mended and there is a conception of unity and symmetry. At the end of the Last Supper, Judas leaves to betray his master, and Jesus continues to tell the Apostles that they, too, will abandon him. From the Last Supper, Jesus proceeds to the Garden of Gethsemane, where there is a last moment before he is apprehended, furthering the division between Jesus and his teachings on Earth. The Last Supper could represent one of the last moments where the divine legacy of Jesus was present on Earth, and in honoring this message, Christians feel they are honoring Jesus.