Agree with LouC that it does sound like the OMC ESA system.
Do you have one of these (on top of the engine where the shift cable attaches)?
If so, you do have the ESA system.
The grey triangular part at the lower left kicks up or down as you shift into forward or reverse. As it does, it pushes the little switch with the roller arm. That switch intentionally cuts your engine rpm down (and makes it run rough for a second). After the shift cable finishes moving, the grey triangle is supposed to spring back to center, releasing the switch, and the engine returns to normal.
As LouC said, if your shift cable going to the lower unit is stiff, then the lever may not return to center right away. Shift cable is most likely cause, but weak or broken spring here could also do the same thing. Adjustment of shift cable could also help, but look up the whole procedure for adjusting the shift mechanism before attempting, so you don't make it worse.
Also, with this type of OMC shifting mechanism, you should not be timid when shifting. I had learned to push the throttle/shifter lever rapidly from nuetral to forward idle or reverse idle. It can even help to push about 1/2" too far, then quickly return to forward idle before the engine responds. However, this is a temporary fix that might help get you through the season, but eventually you will want to change the shift cable. (requires removing the upper/lower unit).
