I asked about when Constantinople became a patriarchate on a blog entry at Midwest Conservative Journal and William Tighe commented:

It took Rome a long while to accept, and that rather offhandedly in 534, that the Constantinopolitan council of 381 was “an ecumenical council” — entirely understandably, since it had been convoked merely as a synod of the eastern portions of the Roman Empire. In 382 a similar western local council was held in Rome, which accepted the Nicene Creed as modified by or at the previous years’ council in Constantinople, but rejected that council’s attempt to put Constantinople on a parity of sorts with Rome, going on to insist that Rome owed its primacy to “the divine voice” and not to the decrees of any council; and it rejected out of hand the eastern council’s proposed solution to the schism in Antioch (between “Nicenes” and “ultra-Nicenes”) that had been going on for 30 years by that point. Leo the Great insisted that there were only three ecumenical councils: Nicaea, Ephesus and Chalcedon, and he rejected, explicitly, Canon 28 of Chalcedon, which again tried to give Constantinople a kind of coequality with Rome and, tacitly, the promotion of Jerusalem to patriarchal status. The letter in which the “Formula of Hormisdas” (519) was embedded made mention of only three councils as well. It was in Justinian’s reign that Rome began to cease to object to Constantinople and Jerusalem’s de facto status, but it was not until the Fourth Lateran Council in 1215 that Rome ratified a canon giving the number of patriarchates as five and their order as Rome, Constantinople, Alexandria, Antioch and Jerusalem.

Also, for a very long time Rome regarded the whole notion of “patriarchates” as an Eastern affectation, and not at all relevant to its own self-conception. The first Roman mention of Rome as a “patriarchate” comes in 642 (as “Patriarch of Rome”) under Pope Theodore I (a Greek born in Jerusalem), and it is notorious that Rome never regarded the title as significant, even after adopting it. And, of course, Benedict XVI, with that quiet candor that seems a hallmark, dropped the patriarchal title entirely shortly after becoming pope.