I have no problem with approaching someone the next day and saying "hey that party last night was a bit full on, maybe you can tone it down next time" or whatever. But if you want it resolved at the time, the best thing to do is let the police handle it. That's why they ask that you let them do so.
I know my neighbours and if they were annoyed by my music being too loud (I doubt they would be, I have no interest in playing music so loud I can't hold a conversation on my own property and I would probably tell them beforehand if I was having a big party) I'd be fine with them popping over and saying 'hey it's late, can you turn it down a bit?' or telling me the next day things went on a bit late or were a bit loud.
If they called the cops on me then decided to drop by the next day to let me know 'hey, that party was a bit loud huh?' I'd be pretty annoyed.

