I cannot find the exact quote of Augustine. Here are a couple of other patristic texts that I have found:
Pope Julius I
"[The] judgment [concerning Athanasius] ought to have been made, not as it was, but according to the ecclesiastical canon. It behooved all of you to write us so that the justice of it might be seen as emanating from all. ... Are you ignorant that the custom has been to write first to us and then for a just decision to be passed from this place [Rome]? If, then, any such suspicion rested upon the bishop there [Athanasius of Alexandria], notice of it ought to have been written to the church here. But now, after having done as they pleased, they want to obtain our concurrence, although we never condemned him. Not thus are the constitutions of Paul, not thus the traditions of the Fathers. This is another form of procedure, and a novel practice. ... What I write about this is for the common good. For what we have heard from the blessed apostle Peter, these things I signify to you" (Letter on Behalf of Athanasius [A.D. 341], in Athanasius, Apology Against the Arians 20Ã¢â‚¬â€œ35).
Council of Sardica
And this case likewise is to be provided for, that if in any province a bishop has some matter against his brother and fellow-bishop, neither of the two should call in as arbiters bishops from another province.
But if perchance sentence be given against a bishop in any matter and he supposes his case to be not unsound but good, in order that the question may be reopened, let us, if it seem good to your charity, honour the memory of Peter the Apostle, and let those who gave judgment write to Julius, the bishop of Rome, so that, if necessary, the case may be retried by the bishops of the neighbouring provinces and let him appoint arbiters; but if it cannot be shown that his case is of such a sort as to need a new trial, let the judgment once given not be annulled, but stand good as before. (Canon 3)
If it seems good to you, it is necessary to add to this decision full of sincere charity which thou hast pronounced, that if any bishop be deposed by the sentence of these neighbouring bishops, and assert that he has fresh matter in defence, a new bishop be not settled in his see, unless the bishop of Rome judge and render a decision as to this. (Canon 4)