That's a good point. The difference may be the engine RPM's are dropping close to idle when shifting whereas when driving the RPM's are more constant.
How is the idle after starting or when parked in neutral? Smooth? Is it the gas pedal you're tapping to keep it going?
One thought is the Idle Control Plunger in the throttle body. They get gummed up and stuck sometimes. It may be fully closed and slow to react. You'll see it if you remove the intake tube on the throttle body, it's electrically driven. No need to remove the plunger yet but try spraying some Gumout type product in there. Clean out all the tar and residue you'll see in there.
Again this is just a guess and a cheap fix to start with. Also check around the clutch pedal for any hanging / loose wires which may be grounding out or stretching when the pedal is depressed. You would notice that when idling too.