Don't worry about being a non-drinker.
There's a bit of joking around on this site about different guys' capacity to drink, or not drink, but it is mostly good natured.
I got hammered last night (not in Thailand) for the first time in a long time, and it served as a useful reminder to me that I don't need to have a skinful to have a good time.
In fact, if you're taking a friend home that night, who wants to be super mao anyway? Lay on the bed and pass out? Puke your guts up in the crapper? Not my idea of a fun end to the night.
And from the bar's perspective (just taking a guess here), they are probably happier to see you drinking Cokes all night, as the margins on the watered-down refill Coke in Thailand are probably higher than a bottle of similarly-priced beer.