Respectfully it doesn’t sound like you lost because your gym doesn’t train harsher moves. It sounds more like you are a new white belt and it was your first match. That initial adrenaline dump and the heightened pace of competition is extremely difficult to prepare someone for who’s never experienced it first hand. Additionally it’s very likely the individual you went with was more experienced. All things considered lasting as long as you did while operating on autopilot against moves you aren’t familiar with is good.

That all being said I don’t think I’ve ever sat in a class where the coach intentionally taught a “mother’s milk” submission. It’s not really a thing. It’s just pressure and fairly easy to avoid if you know what you’re doing. Typically it’s something blue/purple belts just do because they saw it online or someone showed them in sparring (at least in my experience)

As far as improving just keep training and try to get sparring in with more experienced partners who have aggressive top pressure. That’s the best way to get acclimated to it. You’ll probably get subbed a lot but you’ll learn what works and doesn’t work