Ceiling fans are often wired for two power sources, one to the light and one to the fan. There may or may not be a wall switch for either. One standard way to wire this is to use four-conductor cable, with the additional "hot" power coming on the fourth wire. If you had noted how the fan was hooked up before you dismounted it, that would have helped. But, assuming that this was done by someone who had some vague clue about house wiring...
In the US, the color convention is Black for hot, White for neutral, Green (or, sometimes, uninsulated) for safety ground, and Red for "secondary hot", which may be used for different purposes in different situations. For the ceiling fan, they may have used black to power the light and red to power the fan, or the other way around.
So: In your case, where there's only one switch and it used to control the lights, I suspect that it's in the red circuit rather than the black circuit. You could check that by turning the power off again, opening up the switchbox, and seeing how wires are connected there.
Or you could go for the empirical: Turn power off, dismount the fixture, wire the fixture's black to red, cap the now-unused black in the ceiling, close it up, turn power back on, and try the switch. I'm betting that will do the job.
(Personally, I'd hook a meter across red and white and confirm that red is the switched line before re-attaching the light fixture, but I admit I'm a bit paranoid.)