Krillin, Tien, and Yamcha were actually more useful in DBZ than they were in DB. Let's take a quick recap of their actions:
Yamcha: Didn't accomplish ******** in Dragon Ball. He never beat a villain (excluding that one invisible guy, but he wasn't really a villain. Besides, Yamcha would've lost if it wasn't for Krillin's quick thinking.), and he never could make it past the first round in any of the World Tournaments. The most he did was tell Puar to cut Goku's tail off. And no, he didn't actually beat Goku when they first fought. Goku wasn't even at full strength because of his hunger, and Yamcha ran away before they could even finish the fight. In DBZ, he manged to beat a Saibamen (while getting himself killed in the process, but meh), and he saved Goku's life when he took him back to his house to give him the medicine for his heart disease.
Krillin: Barely accomplished ******** in DB. He never beat a major villain, and the most he ever did was win two World Tournament fights (one of which he wouldn't have one without Goku's advice) and help Yamcha by coming up with his "nosebleed" idea during Baba's Torunament. In DBZ, he not only managed to kill the majority of the Saibamen, he also managed to start a family, and bang one smoking hot babe.
Tien: Once Tien turned good, the only thing he accomplished in DB was saving Goku from one of Piccolo's attacks. That's it. In DBZ, he did the most badass thing ever when he went up against Cell using all of his strength just to stall him, almost getting himself killed in the process. Sure, Cell absorbed 18 anyway, but we have Vegeta and Krillin to blame for that.
So yeah. They may of had more screen-time in DB, but screen-time =/= usefulness.