God is saying not only that he is omnipotent, all-powerful in and of himself but also that he is the fountainhead of all power and all authority in this world. And so the devil himself is subordinate and dependent upon God for any power or authority that he exercises in this world.
The question you're raising is not unlike the question the prophet Habakkuk asked when he stood in his watchtower and complained against God because he was watching a foreign nation, known for its unspeakable wickedness, attacking and slaughtering the Jewish people—God's own people. Habakkuk reminded God that God was too pure to even behold iniquity. How could God allow this alien power, this wicked power, to be used in such a fashion? God basically said, "Wait a minute, I have not used this enemy nation as an instrument to punish Israel because Israel is more wicked than this other nation. I'm just making use of this nation to chastise my own people who so richly deserve it. But this other nation will get theirs." That's why we have to be very careful about saying that God is always on our side. He may raise up China to punish the United States as an instrument of judgment against us—because all power is in his hands.
When I was studying in Europe back in the sixties, even though it was twenty years after the end of World War II, the bookstores in Amsterdam were filled with literature about the Second World War. The memories were still very vivid and keen to these people, who suffered so much more than we in this country suffered at that time. I remember reading a book that was a result of the release of earlier classified documents from the archives that was titled Hitler, the Scourge of Europe, in which private documents of Hitler's were photocopied and printed. One was an early entry from his diary, in which was scribbled in Hitler's own writing: "This evening I have made a covenant with Satan." He wasn't just kidding. There was a serious effort by Adolf Hitler to engage the assistance of the prince of darkness in the programs he set forth. Obviously that was all happening under the sovereignty of God. God has his reasons for allowing that to happen for a season, but obviously he reserves that moment when his powerful judgment falls on Satan and on people like Hitler, and God's righteous power is ultimately vindicated.