I do think that I'm a better marksman than the results that I achieved.
You may want to think about that statement. You may be good with a rifle but shooting a handgun is a whole different ball of wax.
The best advice I can give you is to start out SLOWLY. That means taking your time with each shot fired and pulling the trigger in SLOW MOTION. If you are concentrating on pulling the trigger very slowly and keeping the sights aligned on the target you'll find that it's very difficult to anticipate exactly when the trigger will break. If you do this, you may find that you have a "hitch" when you think the gun will fire but it didn't.
That is called a Flinch and every centerfire handgunner has to deal with a flinch at some point. For me the solution is to spend a bit of time in Slow Motion and concentrating on staying completely relaxed. One I stop trying to anticipate when the gun will fire I can then start speeding up.
Finally, I would suggest that you engage in a bit of shooting from a benchrest. If your range offers sandbags grap one and plant your hands on top of that sandbag. If they don't have sandbags, take and old towel and wrap it tight with duct tape to make your own rest. BTW, you can shoot from a hard bench but a lot of that will tend to beat up your hands. Shooting from a rest will serve two purposes. One is that it will give you a much better idea if your gun is shooting to the sights. Two, it's a great exercize to engage in to develop and refine your trigger release skills. Finally, it's encouraging to see that you can shoot really small groups, even if it is with a bit of support.
BTW, the standard distance for sighting a centerfire handgun is 25 yards, or 75 feet. With most centerfire calibers sighting at this distance will result in a gun that groups within an inch of the sight from 10 feet all the way out to 120 feet or even more provide the ammo is loaded to standard pressure.
Finally, one additional thing you may want to remember. That is Bore Transit Recoil. This is the deflection of the barrel that occurs under recoil while the bullet is transitting the barrel. As a result of this, heavier bullets that spend more time in the barrel due to lower velocity will shoot HIGHER to the sights than a faster moving lighter bullet. It's why when someone complains that their gun is shooting high/low, many will respond by asking the bullet weight being used.