Do spell targets know they were targeted if they make their saves?

A lot of spells in D&D 5e either work or they don’t, with no visual or audio effect. If your target cant see or hear that you are casting a spell, and they make their save for that spell… do they know that they were targeted? Do they "feel" it?

I ask because it seems that the only thing that counts as an attack in 5e is something with an attack roll. If that’s the case a lot of shenanigan’s can happen, with players claiming their spell meant to immobilize or even kill a foe, was not an attack and should not have provoked the target.
Is there an "official" way to handle it?