I think the OPs issue goes beyond just getting things down smashing a dummy. I mean, I know it's important to get rotations down to the point that you don't even think about them, but I think it's actually feeling competent doing the DPS dance during an instance. It can be tough to feel confident playing the role of DPS when it's out of your element. I can definitely relate playing NIN when I usually heal or tank instances.

As a healer or tank, any DPS you dish out is a contribution. You can optimize here too, but as DPS it's your job to put out as much as possible, and when there's downtime due to mechanics, derps, learning the fight, etc. it can be a little discouraging knowing that your DPS is plummeting. It's a similar feeling when I tank and lose aggro, or someone dies that I could have saved as a healer. I can't speak necessarily for the OP, but I just don't have enough experience as the DPS role to identify the DPS loss that just can't be helped, and feel like there is always something I could be doing better.

What I tell myself and advise the OP is practice, practice, practice. It's how we good at anything, and the experience will come with it. Well... hopefully! OP has already expressed a desire to learn and play correctly just coming here, and that's a good thing.