I own an '04 GTP. A trusted mechanic friend told me that there should be a decal inside the panel door to the gas tank that indicates the car requires premium gas. Mine does not have this. I've continued to use premium gas anyway but with the astronomical cost of fuel I think I'm about to see if he's right.
Yes, you must use premium fuel due to the higher compression of the engine from having a supercharger. A decal on the panel door of the gas tank could have been taken off or fallen off. Do not rely on this. Your owner's manuel will tell you to use premium (91 octane or higher) in your vehicle. If you think the price of gas is too high in order to do so, you should not own this type of car.
While the above is good advice (not to trust the sticker on the fuel door) it is not 100% correct. I own a 2004 GTP Comp G and the 2004 model and above does not REQUIRE premium fuel, it says so right in the owners manual. If you use 87 oct fuel and you hear eninge knock I would switch to higher oct fuel. This is not true for 97-03 GTP's they require premium fel.
I put 89 in my 04 the other day because that's all they had. Ran fine.... I'm sure it wasn't making full power but no engine knock or any other problems came up.