Firstly, you're probably playing with too much treble in your sound. Secondly, try not to hit the strings too hard (turn your amp up and play softer instead). Thirdly, concentrate on damping with both hands. If you're not playing a string, you should have a finger damping it, and that can be from your left or your right hand. A rule of thumb would be, if you're playing the E and A strings, your left hand should be damping the D and G strings and if you're playing the D and G strings, your right hand should be damping the E and A strings.