You are not spacing or comboing properly.
Peach is often cornered in this matchup and getting a dash attack is not that easy, you are probably not making a good use of your Nair or again, not spacing it well enough.
Contrary to popular belief, Peach dies. DThrow to Knee is pretty dumb and in most stages, she is dead around 90~100% assuming you are not kneeing her across the stage.
She has a chain grab from 10% to 69% (a convenient number) and you can jump out of it after it (you didn't do you homework right ?)
Falcon is heavy enough that she should die from the Kill Throw itself till like... 160% ? DI that dude.
"downsmash edgeguard"
"downsmash in neutral
"I loose access to stomp knee before it kills"
"I cant retreat to shield"
:|
>:|
Yes, you are being outclassed and it's there is no shame in being outclassed.
There is shame in lying to yourself and trying to convince yourself that you have no options without trying harder to overcome your limitations (specially when your limitations seem like homework tbh)
It's ok to admit you are not as good as you think you are (ego is a ***** and it stops you from improving), but a lot of what I'm reading is just you getting outplayed or doing dumb **** and getting roflstomped by a character that gets fed out of people being dumb.
Try to... you know... out maneuver the guy or be less bad (make less mistakes and not getting dsmashed in the process) ? When you say you win neutral, do you even know what is neutral ? That is the situation where Falcon should be shining (and also, the hard part of playing Melee) and specially, ****ing up floaties.
You would probably have the same complaints about Samus or ICs ("ROFL, it's hard to L Cancel against 2 shields, Shield Grab is so guaranteed and wobbling takes 0 skilll!!!!"). But your personal experience and struggle with the matchup doesn't make everything you say true. Studying, practicing and specially thinking about the game would make you better (getting better without the controller in your hands is essential) and I doubt you train combos on Peach bot to have better execution in your upair strings.
If you are here to ask for advice, please be open minded and don't belittle your opponent. If you think he is bad, what are you if you keep losing to him, specially in a bad matchup for him ?
Read this
http://meleeiton.me/2014/02/20/training-tools-how-much-can-you-punish/ and watch this video of a known pro who is DSmash happy getting ****ed by a Falcon
https://www.youtube.com/watch?v=F7WSLaQKwV4
A lot of this might sound bashing (which kind frankly, is. I'm a terrible person), but improving in fighting games is not about controlling your character and winning matchups. That's the easy part. The hard part is to apply the mental game and thinking critically on what are you doing wrong in the process (specially in between stocks), and I think you don't have a grasp of that, otherwise you would've thought about 90% of what I've said yourself.
Anyway, I hope you take this all with a grain of salt and good luck on the quest of improvement.