Well, missiles by themselves can't do much, sadly. I was a missile fan too, but desisted in using them pretty much just after I fired them off for the first time.
To better explain:
I had recently jumped into the game, and did some missions to earn a bunch of credits. I bought an eagle (Gotta love the design), and had in mind to do some sort of "Fighter Jet" loadout. I went for two C1 gimballed beam laser and then I wanted to fit a missile rack on top. I had in mind something like "The beam lasers will burn the shields down quickly, and the missiles will take down the hull pretty fast". After I tried them, though, I had the same problems you had with them. So I simply swapped them to a multi-cannon.
All in all, they are pretty useless and never used on player's ships. The only missile that can do some damage is the Torpedo Pylon, but Frontier made that thing so pricy and unfit for battle. You get one shot and only one shot that costs you 15k C. Each time to reload, and I don't even know if chaff or point defences or even electronic countermeasures can make it lose lock. We should be in the age of super advanced technology, but how these missiles are designed seem to remind me more of the early days.
Don't get me wrong, Frontier did develop a good missile. The Pylon is a good missile, and it should be how the basic missile should be in year 3300. I like the fact that missiles don't do damage to shields, so it prevents people from just spamming them over and over, but I think that if we have super fancy tech stuff, we should have good missiles to use too. Unless the Pylon has its ammo capacity increased the only good missile will be just as obsolete as the others. We then would have fairly usable missiles, Cluster bombs and even fancier stuff like Emp missiles that disrupt modules causing the ship to malfunction or shut down so we could capture targets, a non lethal way to deal with things, or can be used to get tactical advantages on the foe or even fancier stuff, but maybe the developers don't want. Maybe they fear they'd be overpowered (When C3 lasers/Plasma accelerators annihilate stuff easily if used correctly), or maybe they made them obsolete to show how new war tech is better at destroying stuff. Who knows.