there are many muting technique's and you need to find what works for you in different applications. You may need to mute with your palm, or lay your thumb accross the strings. You also may need to use the fretting finger to roll off one string and remain in contact with it to mute it (arps) while playing another.

The best way to determine the situation is to go very slow and see where the noise is. From there you can determine the method to control it.