Short version: Work on your combos, learn when to attack and when not to attack, and don't get stressed out.
Long, paragraph form version:
I don't really play Satsuki, but there's some general things you can work on, firstly and most important that you work on your BnB combo (Bread n Butter combo, the one you'll try to connect most of the time). After a connected 2C something like 5C 623B into her OTG loop should be second nature. You could have won most of those matches if you simply increased your damage output, not to mention that ending her combos with an airthrow sets her up for a nasty 4-way wake up game to continue the pressure (after the airthrow you can do a super jump towards your opponent and you can either attack with j.C as they wake up or land with 2a/2b whatever, or at the last moment you can airdash back then do the same j.C vs 2a mixup). Spend some time in training mode if needed.
Other than that, learn when you can and can't punish your opponent. There were a couple of moments in the match where you missed some really obvious chances to punish Nero, like when he launched a deer or did EX crows when you were right next to him. Note that Nero is very vulnerable during the beginning of his summons, and also note that while your in the middle of throwing your opponent that you're invulnerable to damage, so you can start a combo into one of your many throw specials, which if timed right will let you let you dodge the deer/crow/plant whatever and finish your combo (although in the case of the crows you were so close to him that could have done whatever you wanted and still dodged the crows, since they travel pretty far away from Nero). Also note that Nero can't do an attack directly out of his dash (his teleport thing), and a badly spaced dash is an good chance for you to get on the offensive.
Another thing, be careful with spacing. Nero has a lot of range on his moves, and this coupled with his summons means he can control a lot of space. Fortunately Nero has a lot of punishable moves if they're used incorrectly, so the key to beating him is to bait him into doing a bad move that leaves him open and then punishing him for the mistake. Doing this means knowing the range on both your moves and your opponents. Unfortunately I don't really have enough experience to give you solid tips on this other than just play this guy a lot, but I think you were doing pretty good in this area as it is. At a distance, you showed good knowledge of the speed and distance of your moves and managed to get past Nero's range a good few times, it's just that once you got "in" you had a hard time finishing your blockstring or combo and you gave the Nero a chance to back up and set up his offense again.
Lastly, don't give in to pressure. A lot of time players (especially me) know what to do in a given situation, but when the time comes to act they can't because the pressure is too much, and they either perform stupid moves out of desperation, or perform their intended move incorrectly. I'm not sure if this applies to you, but it's something to think about. Nero is a pretty annoying character to fight because his range and summons can lock out your offensive options, but he doesn't really win until he lets that get to your head. One of his major downsides is that he deals crap for damage, so you can afford to take a few hits. Just don't let the pressure get to you, then make a chance to get in and start rape. If this is problem for you, the best advice I can give is to just play a lot and condition your mind to deal with it.
It just occurred to me that you were maybe playing online, and made mistakes because of lag. If that's the case, then in addition to the above try to find matches that don't lag like crap.