Sodano, as dean of the College of Cardinals, celebrated the funeral Mass for Cardinal Law Dec. 21 at the Altar of the Chair in St. Peter's Basilica.
In his homily, Sodano said, "unfortunately, each one of us can sometimes lack in fidelity to our mission. That is why, at the beginning of every Mass, we say the 'Confiteor,'" the prayer that begins, "I confess to almighty God and to you, my brothers and sisters, that I have greatly sinned."
Law died in a Rome hospital early Dec. 20.
Pope Francis, as is customary for the funerals of cardinals who die in Rome, arrived at the end of Mass to preside over the final commendation and farewell. In the Catholic funeral rite, the final commendation and farewell are formal prayers entrusting the deceased to the mercy of God.
The pope read the prayers in Latin, sprinkled the cardinal's casket with holy water and blessed it with incense. But he made no remarks about the cardinal or his life.
In his homily, Sodano told the small group of mourners that Cardinal Law had "dedicated his life" to the church with 56 years of service as a priest, bishop and cardinal "of the great diocese of Boston" before his appointment as archpriest of Rome's Basilica of St. Mary Major.
"It was precisely here in Rome that he closed his eyes to this world to open them in the light of eternity," Sodano said.
Callista Gingrich, who was about to present her letters of credential to Francis as U.S. ambassador to the Holy See, and her husband, former House Speaker Newt Gingrich, were among those attending the funeral.