Yes and no - I main a tank, a paladin even, which meant til SB you were basically told: "Your class is not capable of dealing damage anyways", so I honestly never cared about FFlogs or seeing my numbers or anything like that. Its slowly changing now, but as tank I also take into consideration that there is more for me to do than just deal damage, so I dont sweat about my dps-numbers that much, as long as I know that I did the best I could, tried to improve and performed my main-job well (holding aggro, positioning the boss well, mitigation).

I remember three instances (höhö... sorry...) though when I felt pretty bad about my performance and the feedback I got - two of them rather old, when I was still learning, so they dont completly count, the last one at the end of HW when the problem wasnt really me...
But, well, lets share all of them:
1) 4 years ago, decided to help out some guys with Brayflox NM - they were shouting for a tank (no PF back then) and I offered... and well... I couldnt tank that last boss. Couldnt get out of the breath-AoE (my lagw as horrible back then and I'd never bothered learning to dodge because I had noticed early on that I'm not able to get out of AoEs anyways) and the scholar couldnt dispell the poison. Killed me several times, we wiped two or three times and in the end didnt clear the dungeon. Until then I hadnt felt confident about my tanking, but I was at least convinced that I was doing "good enough" - I had cleared that dungeon before, but apparently only because my WHM-friend back then had Esuna and made up for my mistakes.
2) Cutters Cry - first boss. Again, I was still new and had answered a shout (or some randoms tell? I dont recall). Tanking again. We had no idea about healer-kite, so I was trying my very best to pick up all the adds... the dps however wasnt good enough to kill them, I was running out of CDs, had no idea what to do - it was stressful enough that I remember it even now, 4 years later. The BLM was complaining he couldnt cast with adds on them, the healer was complaining he couldnt heal against me taking so much damage... we gave up after 40 minutes and I felt as if I had let everyone down without knowing what I could have done better.
3) Nidhogg NM, in trials roulette, with two friends. I had a bad day already. Nidhogg was the current trial back then - I hadnt cleared the EX-mode yet, but we got paired with some people who had and they insisited to kill the adds in the order you do in EX. Thats bullshit. The roaming, not-tankable add should die first since it doesnt put a debuff on, but well... my suggestion to do it that way was greeted with so much hostilty that I left the group - got blamed for not tanking the add and for not knowing what to do (well... I did...) and it just made me feel very bad about my performance.

Oh and for the first 2 or 3 months of playing, I basically was thinking of dropping my sub or just sticking to crafting each time I reached a dungeon...

I know those stories dont really match your experience, since they're not really about DPS... I do play bard on occassion, but most of the time I get paired with people doing so, so much worse than me, that I dont stress to much about that.
I also made the following rule for myself: I dont look at FFlogs. If I want to know wether or not my damage is enough, I'll go and do the matching Stone, Sky, Sea. If I can beat that, I'm okay. It means, my damage/performance is good enough for that content - I'll still push myself to try and get better, but I dont need to put myself down by seeing that other people are doing so much better than I am, when, by the games standards, I'm doing good enough (which is also all I ask if I talk about expectations I have from other people: I fyou do some EX-primals or something like that, be able to beat that SSS - dont care about comparing you on FFlogs).