While core strength will likely be the solution, it may be that you are now overstretching when seated. Consider moving the saddle forward somewhat to counteract. Of course you might not want to go forward a lot as it effects other things, and moving it forward will require some core strength to support the upper body, but it can help the lower back if the pain was from overstretching not an overworked core.
Personally i had backpain riding from having to lean over too much due to a lot of setback on the saddle (tall guy with a history of too small bikes), meaning i was in a quite closed position/folded over. On my road and XC bike a bike fit resulted in moving the saddle forward combined with a longer stem helped way more than i ever expected. For my trail bike the trend for steeper seat angles mean my position over the BB is already forward and long reach numbers means I didnt need a longer stem to still stay comfortable. My core gets more of a workout but the backpain went from being in pain on my 10 mile commute, to riding 100 miles and only pain was in my arse

. Summary, dont just settle with back pain or assume more stretching and core will fix it if you already have reasonable flexibility (which i guess you would if you did ride and lot and did yoga anyway).