If it should happen that someone cannot weep, a single word coming from a contrite heart suffices for God. - St. Thomas AquinasQuite. The Holy Father has made the point that anything we direct towards Our Lord is a prayer. It could be out of some sort of anger, some sort of sadness, or out of joy and thanksgiving. Formal prayers have their purpose, especially in the liturgical life of the Church, but that doesn't exclude asking God in other ways. In fact a "pious invocation" suffices for a partial indulgence. Now, our attitude as St. Thomas notes should change over time, as the life of grace draws us towards perfection. Our hearts should be contrite.
At the Holy Mass, all we should ask for is forgiveness as we offer the sacrifice with the priest. (In the traditional form...) "Receive O Holy Father, Almighty and Eternal God, this spotless host..." at the old Offertory of the host, a theme of victimhood repeated in the Roman Canon: "this pure victim, this holy victim, this spotless victim," accompanied by a triple sign of the Cross in the traditional form.
And why do we do this? Out of love! God's very essence is love as revealed in 1 Jn 4. The Holy Trinity is an eternal relationship of love, an exchange of love between three divine hypostases (often referred to somewhat confusingly as persons in translation, a point my theology professor hammers home. As to our relationship with our creator, who made us in His image and likeness: "For God so loved the world that he gave his only Son, that whoever believes in him should not perish but have eternal life." Thus we offer the sacrifice as Our Lord commanded us to do. We suffer as he commanded us. "Pick up your cross and follow me."
I think this contrasts nicely with a passage from Calvary and the Mass by Venerable Fulton J. Sheen. The bishop explained in the preceding passage that Our Lady at the foot of the Cross is never prostrating as St. Mary Magdalene is.
If Mary could have prostrated herself at the moment as Magdalene did, if she could have only wept, her sorrow would have had an outlet. The sorrow that cries is never the sorrow that breaks the heart. It is the heart that can find no outlet in the fountain of tears which cracks; it is the heart that cannot have an emotional break-down that breaks. And all that sorrow was part of our purchase price paid by our Co-Redemptrix, Mary the Mother of God!-p. 36I highly, highly recommend reading this book. Read a chapter, maybe two each time you prepare for Mass until you finish. It's some of the most fruitful spiritual reading I've ever had. And I'm only just at the chapter on the consecration!