Huntington noted the team considered having Cole miss just one start, but ultimately decided a move to the disabled list was for the best.
"It was a group decision, made in the best interest of the team," Cole said following the Bucs' 1-0 loss to Milwaukee on Sunday. "We'll deal with it, rather than prolong it and hope for the best. It's been gradually onsetting, and I just didn't bounce back the way I anticipated after the last start."
"We felt like it was probably better to be aggressive now, get ahead of it and give him some down time to get that fatigue out of there," Huntington said.
The GM said Cole will be activated when his 15 days on the DL are up, if "everything goes to plan." Huntington added all tests done on Cole's shoulder have pointed to fatigue and made no mention of structural damage.
Left-hander Jeff Locke was called up from Triple-A Indianapolis to start Sunday, and sinkerballer Charlie Morton had his assignment pushed back a day to face the Cubs on Monday in what would've been Cole's next start.
"It's frustrating," Cole said of his first career DL stint, "but hopefully we can nip this in the bud. We've come up with some rehab work, and I feel much better than I did a few days ago. I hadn't experienced anything similar to this in the past. I just couldn't bounce back."
Pirates manager Clint Hurdle said he's seen some "red flags" from the 23-year-old Cole recently. Those indicators included lack of consistency and the volume of pitches Cole has thrown.
In Cole's most recent start, he went 5 2/3 innings and limited the Padres to one run on four hits. But Cole's pitch count hit triple digits before the end of the sixth inning, leading Hurdle to turn to his bullpen.
"He's pitched a little bit less efficient this year than he did a year ago," Huntington said. "He's had more pitches per inning, he's pitching with a little bit more baserunners on a consistent level, which means a little bit more stress. So even before Gerrit made us aware that his shoulder felt a little bit tired, we'd been talking about ... Clint had actually been more aggressive getting him out of the game an inning early vs. an inning later."
Cole has pitched into the seventh inning just once in his past five starts, allowing three runs on six hits to the Dodgers in 6 1/3 innings on May 29. He tossed just 88 pitches in that outing, his lowest pitch count of the season. Cole has thrown 100 or more pitches in seven of his 12 outings this year, and he has logged 205 innings since he debuted for the Pirates almost exactly a year ago, including the 2013 postseason.
"We're just taking it day by day," pitching coach Ray Searage said. "We noticed some things the last time he pitched and just want to be cautious. Stuff like this can happen to a young pitcher. Hey, he's 23."