Grab more and chain grab falco. you get lots and lots of damage on falco with it.
Don't counter and fsmash and dash attack so much. while falco is one of the characters that it's more acceptable to use countering against, you clearly were not doing it right. fsmash has a lot of lag, so you'll want to avoid using it too much against fast characters. Dash attack is just really laggy and punishable.
Don't edeguard with the fair like that, stay on the stage and dtilt, fsmash, ftilt, b, etc., or grab the edge and ledgehop a bair, nair, or dair.
you clearly can dashdance and wd, use it to mix up your approach
don't shield grab falco so much. your opponent didn't look like that good of a falco, but good falcos really can mess you up when you try to shield grab them (it doesn't work so well against space animals).
use fair more than nair. against space animals, fair is often a safer choice because of its speed.