There's no need of tire pressure monitors on a Cessna 172. That's what a preflight is for.
A flat tire on a 172, whether it's a nosewheel or a main gear tire, is not a big deal on landing. I had a wheel completely come apart and separate on landing in a 337 once. It pulled a little to one side, and was perfectly controllable. Not a big deal.
I've had tires fail in much heavier equipment at much higher speeds...also not a big deal.
Think of it as a learning experience. Look back at it and see if there's a reason that tire failed, and there's a way you could have seen it coming or prevented it.
Your preflight checklist does note tire pressures, doesn't it?