Ok, raph some falcon advice. I just watched a little bit of it, but as far as I can tell, he was above you for a good amount of time and you had a lot of opportunity. When a falcon is above you, that is when he is most vulnerable in my experience. Instead of immediately uairing (which i tend to do), try to mix it up. Force him into his shield and then DJ grab or something. Or usmash depending on how big his shield is.
at 1:51, you could have platform drop uaired. It's actually quite useful in this matchup. Although, good edge guard either way.
work on you DI. I am AWFUL at DI for some reason and it's why i get comboed so hard.
when falcon grabs you and throws you, he will likely try the regrab. It takes a while, but you will know whether or not you have the proper amount of space to auto-space yourself with a side-b, like at 2:11. Lots of reward there.
Never get-up attack over 100%.
Uhhh, more of the usual falcon stuff, keep moving u-ftilts, etc. Ohh, almost forgot. Grab. Grab a lot. Grabs are so awesome vs. falcon, its crazy. Tech chase with dair and then re-grab. Tech chase again with either a fair or a warlock kick (covers 3/4 options). After either of these, he should be offstage leading to death (because edge guarding a falcon is not too difficult).
One more thing to keep in mind. Falcon does the annoying wall jump. At 2:34 is one example of this. When he is close to the wall, there is a 99.999% chance he will do this. When he does, jab him and dropzone uair. It typically works for me.