Replacing ceiling fan with regular light and new fixture won't shut off
... it was supposed to be a comment but I don't have enough rep to do that.

It looks like you have connected the 'live' of the former fan (that almost surely was turned on by pulling a cord) to the 'bulb' cable.

My suggestion is open the wall switch and taking note of colours: you have to connect to the light fixture the cable of the same color as the one coming from the switch

... my guess is that red was coming from the switch and black was the fan's 'live'. so just swap back with red and all should work (at worst the light won't lit)

PS: remember to insulate the unused cable

EDIT: my guess was right: black is the live (from brakers) and red is the swiched line. swap black cable (on the fixture) with the red one and your issue willbe solved

SO:
White: neutral (common)  

Black: Live (uninterrupted) - not to be connected for lighting  

Red: Live (interrupted by the switch)