You may already know some of this, but I'll type it up anyway.
I spotted some bad habits in there and they're reasonably easy to fix, so here they are:
Sitting in shield and wait for an approach.
This is one of the most common bad habits. You are giving up control of the match in the effort to perform the "best" low level strategy (shield grab). The falco was calling you on it every time. Break this habit ASAP, it's only going to get worse.
How to improve: Try to remain mobile. Practicing wavedashing helps, but also think about staying airborne as much as possible (with opportunistic ducking/crouch cancelling, of course).
Spamming bair repeatedly in neutral.
This isn't always a bad thing, but when you're just sitting in place doing it, you become predictable. Near the end of the match the falco could clearly tell that you were only going to bair and took advantage of that fact to beat you. You can throw out more aerials than just bair.
How to improve: Try mixing it up with autocancel nair or rising fair, they are both long duration options that cover a lot of situations. Shorthop bair definitely has its place, so don't stop doing it. Just try to be less predictable.
Trying land on top of your opponent with an attack whenever you're above them.
This is another common bad habit that earlier players get into. Puff is a character that is at a distinct disadvantage when other characters are below her. The falco was using this to his advantage and hitting you with his own bair and uair. He did not choose too optimally, but if your opponent had been playing fox this set would not have been close at all.
How to improve: Treat every fall like you're in danger. Try to get as far away from your opponent as possible and refresh your jumps. Try throwing out nair on your way down (and away) from your opponent to discourage an approach.
Not going for the ledge when your opponent is offstage.
Ledgehogs are super-duper easy ways to take stock from your opponents, especially at lower levels. If you are not super comfortable chasing your opponent off the stage you should always go for the ledge since it reduces their options to on stage or faking you out and and getting the ledge.
How to improve: Start taking the ledge whenever your opponent goes off stage. Do not give them control of the ledge as it can be hard to remove them from there. Puff is arguably the best character on the ledge, so it's important to take advantage of this.
Not taking advantage of platforms.
Platforms are FANTASTIC tools to take control of a match. They can prevent you from getting camped out by opponents and give you free followups. When your opponent lands on a platform, they are instantly in a bad position. You now know exactly what options they have and how much space they can cover.
How to improve: Practice punishing landings on platforms or retreating there when your opponent is staying grounded. Practice using platforms to refresh your jumps so you never have to go down to the part of the stage where you're at a disadvantage.
Only using uthrow.
There's no denying that uthrow > rest is a fantastic way to kill an opponent, just keep in mind that above a certain % it's no longer a viable option. Even at low % sometimes a back-throw can set you up for a nice ledge punish that uthrow would never have given you the option for. Additionally, since uthrow > rest basically only works on spacies, bhtrowing more will help your game against a lot of characters.
How to improve: Grab some bots or a friend who is good at recovering and practice bthrowing them off the stage and then punishing their recovery. This also doubles as ledge taking practice, as a good pattern to memorize is bhthrow > ledgegrab > punish.
There is probably a lot more stuff I could tell you to help you improve, but I think a whole lot more would become overwhelming.
Good luck!
