What is acceptable damage output? It's different depending on the match weight loadout, and your mech class, but a good rule of thumb is 300 for an assault mech, and 150 for anything else. Those are BARE MINIMUM numbers. You can consider that a break-even point where you've done enough to exist in the match, but you'll need to go above and beyond that to win.
I feel that I've observed enough players to make a broad generalization about the problem. While this isn't true for all the players with a low-damage problem, I have a feeling the leading majority of them suffer from this: Toilet Bowl Aim!!!

Have you ever seen a player that fires their lasers BEFORE they put the crosshairs on the enemy, and then proceed to rake their lasers around like they're drunker than snot? I had the same problem when I started back in CB. There's a realization you must come to in order to solve this problem:
This is not Hawken. This is not BF3. This is not COD. Twitch reaction is not possible in MechWarrior, and you'll suffer if you try to play like it is.
1.) LOWER YOUR MOUSE SENSITIVITY. ****Huge #1 problem****
There's no bigger problem than this one. If your mouse is at 9600DPI and max windows sensitivity, you're not going to have accuracy, and you certainly don't need that speed. The slower the crosshair moves, the more accurate you can be. For MechWarrior, you can bring this down to a VERY low speed. The bigger your mech, the lower the acceptable DPI.
2.) Don't Panic
Take a deep breath and line up your crosshairs. Follow the target for a quick moment and judge the speed before you pull the trigger. This will give your guns the time they need to line up. If your screen has gone dark from missile smoke/bloom, look for the red target box and aim for the middle of it. Don't flail about when you're getting shot at. Yeah it sucks, and you may die in a moment, but you can at least squeeze off a few more rounds into the mech shooting you. This will help your team even if you die. Who knows, you might even take the target down.
3.) Continue to follow the target AFTER you pull the trigger.
Most weapons take a fraction of a second between pulling the trigger and actually firing their round. Lasers deal damage over time. Following the target AFTER pulling the trigger is a great habit to get into, and it'll benefit your damage output with almost every weapon.