It was originally just intended for the East, not as an ecumenical Council and its status as one was not clear for a while–it’s main original purpose was to appoint a bishop of Constantinople. The Creed it produced was accepted by the whole Church including St. Damasus in Rome. However, he disapproved of its canon re-ordering the patriarchates (ie putting Constantinople ahead of Alexandria and Antioch). This is why the Emperor tried to have this done again at Chalcedon, which St. Leo also rejected, referencing this prior rejection. Photius, when defending the authority of the First Council of Constantinople, pointed to St. Damasus’ approval (which was limited to the dogmatic portions).
It’s ecumenical character was affirmed by the Second Council of Constantinople, which was approved by Pope Vigilius (the bishops and emperor knew how necessary Rome’s approval was that they had to coerce Vigilius into coming to that one!). But again, given the context of that Council’s reference (which only notes the prior one’s profession of faith), it is limited to the dogmatic portions Rome had previously received.