this is a very common problem that is due to incorrect left hand placement that's picked up in the first day of playing and never corrected. Except when playing barre chords, the left hand should hold the guitar neck - thumb around the neck, not behind it. This gives the first fingers a good angle to naturally mute the lower strings without having to even think about doing it. The pull-off should be performed by pulling downwards not upwards.

Watch some of the solo videos on this site and notice the thumb and angle of the fingers.