[The HACK]

Engine braking is the effect of the compression of air inside the engine cylinder causing a drag on the driveline. The second you let off of gas on any car while car is in gear*, you are effectively ENGINE BRAKING. The higher the compression ratio, the larger the engine braking effect. The lower the gear, the higher the difference in speed between road speed and engine speed, the larger the engine braking effect.

You should NEVER go from a higher gear to a lower gear then let the clutch out slowly because you're in essence using the friction material on the CLUTCH to act as the brake to bring the engine speed to equal the driveline speed. Imagine the clutch as a big ol brake with the flywheel acting as the rotor and the pressure plate acting as the brake pad. That is exactly what you're doing by letting the clutch out slowly. EVERY TIME you do it, it's the equivalent to dragging on your brakes...Except clutch pressure plate material is about 1/10th as thick as brake pads, and LESS surface area total.

Engine braking is as vital to slowing the vehicle down as brake braking. You should NEVER leave the car in neutral or with the clutch depressed and rely purely on the brakes to slow you down. In ANY car, manual or auto. The driveline is the only thing keeping your engine connected to the drive wheels, if you have it disconnected, i.e. coasting in neutral or with the clutch depressed, there's no way to effectively balance the chassis with throttle when the rear end steps out of line, or if you have to make an emergency maneuver when someone cuts you off, you can't apply power to the drive wheels to escape the lane if you have the driveline disconnected. It's simply bad practice.

The proper, and the ONLY way to drive a manual when slowing down, is to learn how to heel-toe properly so you can always be in the right gear at the right time. Don't rely on keeping the car in high gears, brake only, then clutch in and drop to a lower gear when you need power, because you can't react fast enough when an emergency arise. Human reaction time takes around 0.7 seconds from sight to action, and it'll take the best of us anywhere from 0.3-0.8 seconds to execute a shift. You're looking at 1-1.5 seconds before any action is taken if you have to downshift from 6th gear to 2nd as you're slowing down. That's a freakin' eternity in an emergency.

If you can't properly execute a heel-toe correctly all the time, you should probably stick to driving an automatic. No offense.

*The effect is more pronounced on manuals than automatics, because on an automatic when the engine and driveline spins at different speeds/loads (i.e coasting in gear with foot off gas), the torque converter takes up the slack.