I do the same as Jake, though I used to do it how you do. Either way, the muting of that in-between string is PARAMOUNT. Two things to do to make it easy:
1. Like Dan said, lay that index finger down a little to mute the in-between.
2. Additionally, let the very tip of the “octave” finger, whether it’s ring or pinky, lightly touch that middle string while fretting the octave note. Don’t FRET it, just let the fleshy tip of the finger touch it. That’s more muting.
More muting is better. Both of those techniques can be used in MANY situations to help you play clean.