What Augustine is saying is that the only way we know that the gospel books are from God is because this is taught by the Catholic Church. If we trust the Catholic Church on that point, logically we have to trust them on all other points as well. So if the Catholic Church tells us that the Manichean heresy is wrong, we have to believe that. If the Manichean heresy is not wrong, then the Catholic Church is wrong, and so we would have no basis to believe the gospel books to be from God. For Augustine, our trust in the gospels is part and parcel of our confidence that the tradition of the Catholic Church in general is divinely guided and so authoritative and reliable. It is therefore inconsistent to accept that tradition regarding the status of the gospels but to reject other things that tradition teaches. No Sola Scripturist could make this argument, because the Sola Scriptura position says that only written Scripture is divinely guided in this sense, while tradition is fallible and can sometimes be rejected when it is wrong. Augustine argues like a Catholic, accepting the canon of Scripture on the authority of the Church and also, logically, accepting all other things taught by that same divinely-authorized and therefore guaranteed authority.
A Protestant would say to the Manicheans, "Prove to me that Manicheus is right from the Bible! If you can do that, you win, no matter what the Catholics say." But Augustine says, "You can't prove to me that Manicheus is right from the Bible, because the Catholics say Manicheus is wrong, and the only reason I accept the Bible is because the Catholics tell me to. So if you could prove the Bible supported Manichaeus, you would simply prove the Catholics are wrong and so undermine my belief in the Bible, thus undercutting your own argument."
Here is St. Augustine:
Let us see then what Manichæus teaches me; and particularly let us examine that treatise which he calls the Fundamental Epistle, in which almost all that you believe is contained. For in that unhappy time when we read it we were in your opinion enlightened. The epistle begins thus:--"Manichæus, an apostle of Jesus Christ, by the providence of God the Father. These are wholesome words from the perennial and living fountain." Now, if you please, patiently give heed to my inquiry. I do not believe Manichæus to be an apostle of Christ. Do not, I beg of you, be enraged and begin to curse. For you know that it is my rule to believe none of your statements without consideration. Therefore I ask, who is this Manichæus? You will reply, An apostle of Christ. I do not believe it. Now you are at a loss what to say or do; for you promised to give knowledge of the truth, and here you are forcing me to believe what I have no knowledge of. Perhaps you will read the gospel to me, and will attempt to find there a testimony to Manichæus. But should you meet with a person not yet believing the gospel, how would you reply to him were he to say, I do not believe? For my part, I should not believe the gospel except as moved by the authority of the Catholic Church. So when those on whose authority I have consented to believe in the gospel tell me not to believe in Manichæus, how can I but consent? Take your choice. If you say, Believe the Catholics: their advice to me is to put no faith in you; so that, believing them, I am precluded from believing you;--If you say, Do not believe the Catholics: you cannot fairly use the gospel in bringing me to faith in Manichæus; for it was at the command of the Catholics that I believed the gospel;--Again, if you say, You were right in believing the Catholics when they praised the gospel, but wrong in believing their vituperation of Manichæus: do you think me such a fool as to believe or not to believe as you like or dislike, without any reason? It is therefore fairer and safer by far for me, having in one instance put faith in the Catholics, not to go over to you, till, instead of bidding me believe, you make me understand something in the clearest and most open manner. To convince me, then, you must put aside the gospel. If you keep to the gospel, I will keep to those who commanded me to believe the gospel; and, in obedience to them, I will not believe you at all. But if haply you should succeed in finding in the gospel an incontrovertible testimony to the apostleship of Manichæus, you will weaken my regard for the authority of the Catholics who bid me not to believe you; and the effect of that will be, that I shall no longer be able to believe the gospel either, for it was through the Catholics that I got my faith in it; and so, whatever you bring from the gospel will no longer have any weight with me. Wherefore, if no clear proof of the apostleship of Manichæus is found in the gospel, I will believe the Catholics rather than you. But if you read thence some passage clearly in favor of Manichæus, I will believe neither them nor you: not them, for they lied to me about you; nor you, for you quote to me that Scripture which I had believed on the authority of those liars. But far be it that I should not believe the gospel; for believing it, I find no way of believing you too. For the names of the apostles, as there recorded, do not include the name of Manichæus. And who the successor of Christ's betrayer was we read in the Acts of the Apostles; which book I must needs believe if I believe the gospel, since both writings alike Catholic authority commends to me. The same book contains the well-known narrative of the calling and apostleship of Paul. Read me now, if you can, in the gospel where Manichæus is called an apostle, or in any other book in which I have professed to believe. Will you read the passage where the Lord promised the Holy Spirit as a Paraclete, to the apostles? Concerning which passage, behold how many and how great are the things that restrain and deter me from believing in Manichæus. (St. Augustine, Against the Epistle of Manichæus Called Fundamental, Chapter 5, text from here)
For more on the Church Fathers and Sola Scriptura, see here and here.