How do planes maintain constant speeds at cruise altitudes?
The autopilot pitches to hold the flight level when it captures the level at the top of the climb, so later on as the aircraft gets lighter and wants to climb further, the A/P will lower the nose as required to hold the flight level (the A/P is able to move the elevator through its servo's link to the elevator controls; it can also work the trim if the servo has to hold too much out-of-trim force for too long, to avoid wearing out the servo - in effect it does what the human pilot does, more or less).  It happens very slowly and significant amount of pitch over is not apparent until some time has passed.  

Effectively, AOA is being reduced by the A/P to compensate for the reduction in wing loading.  Because induced drag is being reduced, if thrust is not reduced to compensate for the drag reduction, the A/C will accelerate.  If your clearance requires you to maintain a certain Mach #, this is a problem.

If the jet has an autothrottle system that can be configured to hold a Mach # while the A/P holds the altitude, the thrust is adjusted automatically.  If not, the pilot monitoring at some point will notice the Mach # creeping up, and will reduce thrust in very small increments compensate and maintain the flight planned/cleared Mach #.