Dampen the strings. Tapping is most effectively done with the index finger of your right hand. Since the technique usually involves one string at a time, the thumb and the palm of your right hand should be gently placed over the strings that aren't in use, with just enough pressure to keep them from buzzing.
Turn down the gain on your amplifier. Whether your amp is on the distortion or the clean channel, lowering the gain on the amplifier will decrease the amount of your guitar signal that is amplified, thus reducing the sensitivity of your pickups.
Turn down the volume knob on your guitar. This also will reduce the heat of the signal going into your amplifier, but it's a much quicker solution if you are performing and you can't access your amplifier.
Practice your technique. In general, any new technique that you add to your guitar repertoire is going to become cleaner and more fluent over time as you become more familiar with it. Try to get your tapping technique as clean as possible at slower speeds before trying to tap at faster speeds.