The new President, James Monroe, who was elected in 1816, did not want the European powers meddling in the New World, now that they were no longer distracted by Napoleon. So in Monroe’s Inaugural Address, he said this:
In the wars of the European powers in matters relating to themselves we have never taken any part, nor does it comport with our policy so to do. It is only when our rights are invaded or seriously menaced that we resent injuries or make preparation for our defense.…
With the existing colonies or dependencies of any European power we have not interfered and shall not interfere. But with the governments who have declared their independence and maintained it, and whose independence we have, on great consideration and on just principles, acknowledged, we could not view any interposition for the purpose of oppressing them, or controlling in any other manner their destiny, by any European power in any other light than as the manifestation of an unfriendly disposition toward the United States.
He’s basically making the point that the US had not, and would not, intrude on any of the European disputes between the European powers. He’s also making the point that the US hasn’t interfered with existing new world colonies, which, OK, that’s not exactly true, but the US really hadn’t yet done anything in central America or South America. We had interfered, a lot, with other colonies in North America, and some in the Caribbean, too.
But his main point was that the colonial era in the Americas was over, and that any attempt by the powers of Europe to oppress or control any of the new countries in the New World would be seen as, as he said, ‘unfriendly toward the United States.’