Hell no! It does owe an apology to the Orthodox Church. The Catholic Church pushed the Lithuanian Empire for example to make war on the small nation (at the time) of Russia simply for not being Catholic. And in the Crusades, it conspired with Venice to sack the largest Christian city.
The Catholic Church did not conspire with Venice to sack Constantinople. Read Villehardouin’s history of the Fourth Crusade. The Franks made a deal with the Venetians to provide ships but failed to raise the agreed on sum of money so they had to do what the Venetians demanded. First they captured the Catholic city of Zadar (Zara) in Dalmatia for Venice (for which they were excommunicated by Pope Innocent III). Then they were persuaded by a member of the Byzantine imperial family to intervene to put him on the throne of the Byzantine Empire. One thing led to another and the Crusaders eventually captured and sacked Constantinople, which was a great tragedy, but it wasn’t planned in advance and the pope was certainly not privy to the Crusaders’ plans.