Gagne said that his right arm, which had been diagnosed with rotator cuff tendinitis, would be fine in a few days, but the team couldn't afford to wait that long for bullpen help.
"We were thinking five, six or seven days," Gagne said. "But you can't be short in the bullpen. We're already a little thin out there, and we needed somebody extra."
Having arrived Friday after getting examined in Milwaukee, Gagne will remain with the team for the remainder of its series against Washington. Now that he is sidelined for at least 15 days, he said he will re-evaluate his treatment as needed on Saturday.
The decision to put him on the DL was not made until minutes before the Milwaukee's game with the Washington Nationals, and was done so that Dillard would be able to pitch in that game if needed. Dillard pitched the eighth inning and struck out one in a perfect frame in his Major League debut.
Earlier in the day, manager Ned Yost said he was undecided on which pitcher to send down.
The more immediate concern for the team is the fifth starter's spot, which will be filled by Seth McClung on Saturday. Dave Bush is hanging on in the fourth starter's spot despite a rough outing on Thursday. Yost dismissed the thought of breaking up the two spots among several players.
"That's too radical right now," Yost said. "It seems that we have a lot of guys who did OK one or two times out, but we're lacking the ability to execute on a consistent basis.
"Bush was great in the first few innings, but struggled in the fourth."
Gagne's departure cleared the way for Dillard, who will be able to pitch several innings of middle relief.
Gagne left Tuesday's game with stiffness in his right shoulder before heading back to Milwaukee to seek a medical opinion.
Right-hander David Riske is also on the disabled list with an elbow injury, creating a need for additional relievers in the Milwaukee bullpen.
Michael Phillips is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.