No, I already told you this incorrect. Gregory the Great recognized Constantinople as it was accorded in the Chalcedon canons.
The council was called by Emperor Theodosius, to provide for a Catholic succession in the patriarchal See of Constantinople, to confirm the Nicene Faith, to reconcile the semi-Arians with the Church, and to put an end to the Macedonian heresy.
Originally it was only a council of the Orient. It was attended by 150 Catholic and 36 heretical (Semi-Arian, Macedonian) bishops, and was presided over by Meletius of Antioch; after his death, by the successive Patriarchs of Constantinople, St. Gregory Nazianzen and Nectarius.
Its first measure was to confirm St. Gregory Nazianzen as Bishop of Constantinople. The Acts of the council have almost entirely disappeared, and its proceedings are known chiefly through the accounts of the ecclesiastical historians Socrates, Sozomen, and Theodoret.
The first canon is an important dogmatic condemnation of all shades of Arianism, also of Macedonianism and Apollinarianism.
The second canon renews the Nicene legislation imposing upon the bishops the observance of diocesan and patriarchal limits.
The fourth canon declares invalid the consecration of Maximus, the Cynic philosopher and rival of St. Gregory of Nazianzus, as Bishop of Constantinople.
The famous third canon declares that because Constantinople is New Rome the bishop of that city should have a pre-eminence of honour after the Bishop of Old Rome. Baronius wrongly maintained the non-authenticity of this canon, while some medieval Greeks maintained (an equally erroneous thesis) that it declared the bishop of the royal city in all things the equal of the pope.
The purely human reason of Rome’s ancient authority, suggested by this canon, was never admitted by the Apostolic See, which always based its claim to supremacy on the succession of St. Peter. Nor did Rome easily acknowledge this unjustifiable reordering of rank among the ancient patriarchates of the East.
It was rejected by the papal legates at Chalcedon. St. Leo the Great declared that this canon has never been submitted to the Apostolic See and that it was a violation of the Nicene order.
At the Eighth General Council in 869 the Roman legates acknowledged Constantinople as second in patriarchal rank.
In 1215, at the Fourth Lateran Council this was formally admitted for the new Latin patriarch, and in 1439, at the Council of Florence, for the Greek patriarch.
At the close of this council Emperor Theodosius issued an imperial decree declaring that the churches should be restored to those bishops who confessed the equal Divinity of the Father, the Son, and the Holy Spirit, and who held communion with Nectarius of Constantinople and other important Oriental prelates whom he named.
Gregory the Great, following the example of Vigilius and Pelagius II, recognized it as one of the four general councils, but only in its dogmatic utterances.