"He pleaded his case. But at the end of the day, this is probably the right thing to do," said Black.
Hudson suffered the strain in the first inning on Tuesday, when he doubled to center field. He thought the injury might have occurred as he was starting to make a push for a triple.
"I was going three [triple] out of the box," Hudson said. "When I hit a ball in the gap like that, I'm always thinking three."
Hudson said on Wednesday that his hamstring was feeling better, though the severity of the strain led the Padres to take the cautious route.
"With the history of hamstrings, it was probably going to be seven to 10 days before he could play at a level you need to play at," said Black. "Even with that, the risk factor of re-injuring it is high. We felt we did the thing that made the most sense."
Hudson was on the 15-day disabled list in 2004 with a left hamstring strain while he was a member of the Blue Jays.
The Padres purchased the contract of second baseman Logan Forsythe from Triple-A Tucson before Wednesday's game against the Pirates. Forsythe was in uniform for the game.
Eric Patterson got the start at second base in the series finale.