Will using mid-grade gas on a premium damage or make my car run worse?

Nope… You Can Run The 89 Or 93 Octane With No Worries Of Engine Problems.

it does damage the engine, and decrease power. octane ratings and cylinder compression go hand in hand. The higher the octane rating (up to 100) the more it can be compressed without combusting. If your car says to only use premium gas it is because it has a high compression ratio. FOR EXAMPLE ONLY lets say that your cylinder is 12″ from top to bottom when the cylinder is at the bottom. 87 octane will detonate without a spark when the piston reaches the 6″ mark. 89 octane will detonate at 3″ mark and 93 octane detonates at 1″ mark.
your car engine has a compression ratio of 12:1. so if you use 89 octane gas the fuel/air mixture is detonating (exploding without a spark) before the piston reaches the bottom. it then puts a lot lot lot lot of pressure on your piston the opposite way it is traveling. this causes fatigue and stress on all engine parts and can lead to premature failure.
for a full fill-up using 89 octane only saves you about $1.40. but with increased octane, comes better fuel economy, more power and less damage to your engine. it saves a lot to use the correct fuel.

If it’s like my car that is made for premium it won’t even run on anything but premium. If it says to run 91 or 93 I would run that and nothing else.

OK you wont have a problem. the only cars that will be affected are high performance cars. for example my dad has a supercharged commodore and that NEEDS premium otherwise it becomes very sluggish. so your prelude wont have a problem because its not exactly a performance vehicle ( no offense )

nope but what you really want to know is which octane and brands your car gets the best mileage with way to do that is first stop an dfil lat place you always stop with highest octane set mileage write it down drive til you need to refill at same place use next lower octane one that gets you th ebest mileage right one then do same thing at next place up street then do same thing with places coming home its like say my nissan gets great mileage with shell high octane but gets same with mobil regular you as driver needs to know which fuels your car wants to run on not price not what octane but what gets you the best mileage might even run regular with same mileage.. its what mileage you get none will damage but knowing which gets you farther saves you money

Robert was almost correct.

The purpose of using higher octane gas is because it is more stable. The rating is its resistance to knock/detonation and NOT preignition which is a whole different problem. You could use 87-89 octane but I wouldnt speed around or do any spirited driving.

The higher the compression ratio the higher the engine output (usually) which means you need a more stable fuel because you’re adding more heat energy to the air/fuel charge when you compress. The air filling the cylinders can (load) the air/fuel charge also depending on the VTEC and how aggressive that cam lobe is. What happens when knock occurs is the spark plug fires, the air/fuel charge explodes creating multiple flame fronts inside the cylinder instead of an even smooth progressive burn from the plug outward. This explosion beats on the piston like a jack hammer causing it to oscillate back and forth inside the cylinder. Thats the ‘knocking’ noise you hear. Its the piston skirt slapping the cylinder walls. It can be hard to hear sometimes but you can notice a loss of power. This can ruin the top of the engine by melting pistons, cracking piston rings, blowing chunks of ring lands into the oil pan, and fretting corrosion can occur around the connecting rod and main bolt fasteners (bolts, nuts). It can mess up your bearings also. Lower octane fuel burns faster than high octane fuel. Your engine should have a knock sensor which would ‘retard’ the firing of the spark plug until the piston is closer to the top of the cylinder.