Frieza's underlings weren't very strong. Only Zarbon and Dodoria were somewhat formidable, but even they were only around Vegeta's level.
Zarbon also knew how to transform, but unfortunately, aside from making himself incredibly ugly, his transformation did little to increase his Combat Power. Facing Piccolo, he had no effect on the battle and was ultimately killed cleanly and decisively by him.
Vegeta went after Dodoria. Of those two close subordinates, Dodoria was relatively weaker, yet he was still stronger than Vegeta.
As a result, Vegeta was dragged into a hard battle. He was badly wounded at one point and nearly died at Dodoria's hands, only to be saved by Raditz, whom he had once looked down on immensely.
Vegeta was extremely displeased, but being upset changed nothing. He could only accept the fact that he was still weak and far from his goal.
Clearing out Frieza's subordinates would take some time, so Nappa used that time to place Vegeta in the Healing Device aboard Frieza's ship.
"Luckily, this ship has the newest model of Healing Device. You'll recover before long."
"..."
Vegeta closed his eyes. Though being defeated annoyed him, challenging powerful enemies—even if he couldn't beat them and ended up severely injured—could still let him improve through the trait of gaining Combat Power after recovering from near-death experiences.
While he recovered and increased his Combat Power, Piccolo continued harvesting the lives of Frieza's subordinates. Even without Krillin and Son Goku joining in, and with Yinsen resting, Piccolo and Yoruichi alone did not need much time to clear them all out.
Most of the time had been wasted searching for them. As for the fighting? It had basically all been Instant Kills!
"Tch. Isn't this Frieza supposed to be the Galactic Emperor? Doesn't he have any decent subordinates?"
Piccolo was