You leave a lot of dmg on the table, that's kinda why you lose - I'll elaborate on that later.
Even though downplayers will scream Kitana can't open people up - people always get caught by the second hit low in neutral and that happens a lot. The other guy throws out b1 (I think it is?), it whiffs but he lets the whole string rock, and you get hit by the low. It happens to me all the time. You need to watch out for that.
As for the damage left on the table. You connect and get away with a lot jump-in kicks. You connected with 2 in a row in the final round of the first game - I think you could have followed one of them up with a Fatal Blow (whereas your opponent uses his immediatly after and you lose the first game). And since his anti airs wasnt a threat, and given the fact you connect with a lot of jump-ins - maybe you could have done a jump-in punch instead and get a full combo? And be careful of which strings you decide to finish - you get full combo punished on more than a few occasions because you hit them out of the air, but the followups whiff leaving you vulnerable for a wakeup jab combo.
Maybe it's hard for Kitana I dont know, but having a plan with jump-ins definitely pays off. You see Liu Kangs do flying kicks or bicycle kicks when they hit with a jump kick, Jades do Nitro Kick, seen Jax do an air grab (with bf4) after succesful kicks. Like imagine if you had followed up with a flying forward thingy move you got? that's a lotta damage. And remember how close it was.
Don't be discouraged though. You seem to have the better fundamentals, your staggers worked well, you teched throws. It's primarily these little details that unfortunately add up. Leaving damage on the table, getting hit by too many fans, not managing meter correctly.
It's a bit hard to give match-up advice in a mirror match. It's really about getting the most out of every opportunity