I'm trying to play this song on acoustic and it doesn't sound very good. I play an octave on the third fret and slide down to the second. Then I improvise and and pluck a muted E string a few times . It sounds OK to me but I want to know if there's a way to make it sound closer to the electric version.
A link to the song and you telling where in the tune they are using the harmonics would be nice. And what do you mean with that you played an octave on the third fret?
That is "pinched harmonics" or artificial harmonics.
I wrote a long post explaining it, but I think a link to a video that explains it would be better, oh well 10 minutes of my life wasted
(note that the technique is different whether you fingerpick or flatpicking, and both have various of ways to produce artificial harmonics)
an example of fingerpicked way:
of a flatpicking way: