It almost sounds as though Paul is saying that what Jesus did was not sufficient, but he would never say that. We ought to read this passage in light of St. Paul's other writings, in particular, what he says about the Body of Christ in 1 Corinthians 12. Christ is the Head of the Body. We are members of the Body, joined to Christ. What Christ has done, we the Body are now called to do. When we join our sufferings to the perfect offering of Christ on the cross and at Mass, we play a role in the ongoing work of salvation.
Mary is our model in this. "Lumen Gentium," the Vatican Council II document on the Church, quotes St. Ambrose and states that "the Mother of God is a type of the Church" (#63). She stood under the cross of Jesus and did not scream or try to stop the soldiers from crucifying her own flesh and blood. She shared in her Son’s faith that this act of violence would not be the end, that somehow God would bring great good from it, that God was saving the world through it. She had great faith, but it didn’t take away her own pain and sorrow.
We are called to have that same faith when it comes to our own sufferings. In "The Joy of the Gospel" Pope Francis wrote these encouraging words: "No single act of love for God will be lost, no generous effort is meaningless, no painful endurance is wasted. All of these encircle our world like a vital force" (#279).