It is common for LEDs to glow after they have been turned off. They might flicker slightly for several minutes, or they may produce a low light, only a fraction of their normal brightness, that does not go away. This may be especially noticeable with a concentrated source of light like a spotlight. If you unplug the LED light entirely, the glow should soon vanish.
This glow from the LED lights is caused by residual voltage in the electrical line that powers your spotlight. LED bulbs are made out of a collection of diodes. Just one of these diodes is so efficient that the residual current that still travels your power cord is enough to cause it to light up slightly. While this does not indicate a serious problem, it can wear down your LED bulb and might be annoying for your lighting designs. You have a couple of options to rectify the problem.
If you want to spend a little money to fight diodes with diodes, you can install a zener diode on the same electrical line that the LED light uses. This diode is designed to block residual voltage for delicate electrical components, so it should be able to stop any incoming current from lighting your bulb. Zener diodes come with different values of blocking, so choose a higher value -- enough to block the voltage flowing through your line.
Your LED spotlight is probably already a cluster bulb, made out of several diodes. These bulbs have an advantage because they require a higher initial voltage to start. You might be able to fix the problem by switching to an even larger cluster. This requires buying a new LED spotlight, which can be expensive, but can also solve your problem.