Cardinal Lourdusamy, 90, passed away in Rome June 2.
Jayalalithaa said: "I was deeply saddened to hear of the passing away of Cardinal Duraisamy Simon Lourdusamy, a pillar of the Catholic community."
"Cardinal Lourdusamy was the 4th Indian Cardinal and the first Tamil Cardinal of the Roman Catholic Church and the first Curial Cardinal of Asia outside of the Middle East," she said in a statement issued here.
Jayalalithaa said Cardinal Lourdusamy was the Prefect Emeritus of the Congregation for the Oriental Churches in the Roman Curia and was elevated to the Cardinalate in 1985.
Born in Kalleri village near Gingee in Tamil Nadu Cardinal, Lourdusamy had his early education at St. Ann's in Dindivanam and completed his high school studies at St. Joseph High School in Cuddalore.
He entered St. Agnes's Minor Seminary in Cuddalore and completed major seminary education in Philosophy and Theology at St. Peter's Pontifical Seminary, Bangalore.
Jayalalithaa said Cardinal Lourdusamy after studying further at Loyola College here, was sent to Rome to pursue higher studies in the area of Canon Law at the Pontifical Urbaniana University.
It was during the Papacy of St. Pope John Paul II, Father Lourdusamy became Cardinal-Deacon of Santa Maria delle Grazie alle Fornaci fuori Porta Cavalleggeri in the consistory May 25, 1985, the Tamil Nadu chief minister said.
"The Cardinal's rise from humble beginnings and his service to the church would forever be etched in the history of the world. A man of the cloth, he was a true believer in the fatherhood of god and the brotherhood of man," she said.