Falco doesn't have great throw follow-ups. "Then why grab at all ?" you might ask. Because grab beats shield. It's as simple as that.
Now don't think straight away that Falco's grab game sucks compared to the rest of the S-tier. Unlike them, who need to DD, punish, tech chase etc, you get grabs almost for free all the time ! Because what lasers and pressure do is making them get in shield way more that against other characters, which in turn lets you grab them for super free. And when they start to see whats happening and do something else, you can punish with dair or take their space if they retreat for example. Shine-grab is good because theres no winning answer for them, and shine is way faster than just grabbing so it keeps you safe if they tried to act faster than you.
Then, what to do with a grab ? F-throw offstage is good, preferably at high %. Otherwise u-throw is best. u-throw>fair is great on mid-wheights like Marth at low%. u-throw>shine on fast-fallers at low%, u-throw>bair/shine>bair at high%.
Often you can't really follow-up, instead you could fake an attack by jumping close to them, to bait a move or their DJ : then you can punish them for it. If they don't bite, next time try and punish them at landing, espescially on platforms (shine>wave-land, rising dair, bair at kill%).
Anyway, when you throw them, be it up or forward, you gain stage positioning. You can make holding center stage a huge advantage in most match-ups, so this is good. Exercise to zone with lasers and aerials, keeping them out. They get pressured and will come in sooner or later, but your stage control will force them in shield invariably, letting you grab'em and either get a punish (catch them on platforms etc) or resume this winning situation for you. This is very very hard to deal with against Falco and will get most opponents to make dumb mistakes eventually. So grab is an important tool in this standard game-plan, because it beats shield fair and square, without having to quad-shine pressure into following rolls or something all the time.
All this was to tell you that when your friend told you to use grabs more, what you should understand and put in practice isn't necessarily to do u-throw combos. Instead, figure out the place that grabs hold in Falco's metagame.