My TV's Netflix app doesn't have an option to disable the auto-playing trailers, or even just their sound (short of muting the TV). It's quite annoying.
I have a recent AppleTV, which doesn't have any way to disable auto-playing trailers. Same for my previous STB (Roku). This is a somewhat new feature, so some older STBs and Smart TVs don't have it, but that's just because they can't be updated to the latest version of the Netflix app.
You can disable auto-play next episode across all interfaces and devices in the settings on netflix.com. I just wish there was an equivalent switch for trailers.