I'm not that good at the technical part of playing guitar (despite my teachers' best efforts), but off the top of my head you could try muting the strings with your picking hand right before you take your fingers off. Also, how calloused are your fretting fingers? In my experience the harder and smoother the callouses the less likely you are to get that reverberation you described. Something else that just came to mind...how hard are you pressing down with your fretting fingers? Less pressure, just enough to let the notes ring correctly, might make it easier to lift your fingers without extra noise. One problem I had was thinking I didn't have enough time to move my fingers to the right places so I tended to hurry. Maybe you should try it slowly and deliberately first. Then, as you get smoother at the transition, you could start moving a little faster. Then slowly increase the speed until your at the piece's tempo.
I hope that was at least somewhat helpful.