The TSX's engine is a high-compression engine. It needs the higher octane to prevent pre-ignition/detonation. You can put in lower octane, but your fuel economy will suffer (which will make you have to put in even more gas), and you won't be able to drive your car to its limits (you'll have to drive like a grandma).

It's only a few dollars more to use premium. You get more fuel detergents, you can drive harder, and you get better fuel economy. The few dollars is worth it.