A proper constant current or regulated current supply is going to require an active device... A transistor, MOSFET, or a chip with transistors/MOSFETs inside. And since linear designs tend to be very inefficient (and components tend to get hot), a switching design (with an inductor) is commonly used.
For regular low-power LEDs, we usually don't care about efficiency (and heat is not an issue) we can simply use a voltage-regulated supply and a current-limiting resistor. (The more voltage we drop across the resistor, the closer we come to a constant current supply, and the less efficient the circuit becomes.)
...If the voltage & current numbers on your schematic are correct, you've got less than 1/2 watt going to the LED (current x voltage) with more than 2W consumed by the other components.