You just got an object lesson in how LEDs are non-linear.
Incandescent bulbs are linear once they light. Linear means it acts like a resistor: current draw is in proportion to voltage: half the voltage, half the current, 1/4 the power. An incandescent light would do what you expect.
LEDs have a very steep voltage-current curve: a small change in voltage results in a large change in current draw. You are off the bottom of that chart, hence no light.
The steep curve makes the LED very jumpy, small voltage changes result in big (and damaging) current changes. Worse, the curve changes based on temperature, binning and age. So LEDs are rated at a specific current rather than voltage. For indicators, you can limit current with resistors. For lighting, where you need peak performance, it's best to use an active driver circuit to regulate the current to spec.
ForSuch circuits also lend themselves to boosting or bucking supply voltage to suit the LED. The Joule Thief is a simple, practical circuit that solves the problem of makingdriving a lighting LED work onwith a single 1.5V battery, there is a circuit called a Joule Thief which both pumps up voltage and limits current.
For what it's worth, it's even worse with the third kind of light, arc-discharge lighting: fluorescent, neon, metal halide, mercury vapor, and high/low pressure sodium. They are insulators up until a certain voltage when the arc strikes... After which they are nearly a dead short. Current limiting is mandatory.