Police anticipated potential problems in the city, regardless of the outcome of the National Championship game in Arlington, Texas.
UK fell to Connecticut 60-54.
The city said the post-game celebrations were significantly smaller than previous games.
Firefighters had responded to 12 couch fires and 15 trash fires as of about 12:15 a.m.
Several people were reportedly treated for injuries.
Police said officers would let the crowds thin out throughout the morning, provided there were not reports of life-threatening problems.