Conley, Miami's seventh-ranked prospect according to MLB.com, was called up by the Marlins on Monday, while Morris was placed on the 15-day disabled list.
"It's unfortunate about Morris. Obviously he's a great pitcher and he deserves to be up here," Conley said. "He's got to get healthy and everything, so I just hope not to replace him, but for my time up here, just do my job and continue to do the work that I've been doing."
Conley joins the Marlins after making 10 starts with Triple-A New Orleans. The 25-year-old left-hander is 5-2 this season to go along with a 3.05 ERA.
"He gives us another left-hander," manager Dan Jennings said. "Right now we'll utilize him out of the bullpen. With [Morris] going on the DL with the back strain, I think having a second left-hander right now is a nice option to have.
"Certainly in Adam's case, we saw him all through Spring Training. He was a bullpen arm in college. Flipping back to that capacity should not be an issue."
The 6-foot-3, 185-pounder out of Washington State University is a far cry from where he was just a year ago.
Injuries limited the former second-round Draft pick of the Marlins to just 13 games during the 2014 season.
Conley was sidelined by elbow tendinitis in May. After successfully rehabbing and working his way back into the rotation in New Orleans, he suffered a bone bruise from overthrowing.
"It was kind of a weird deal. I've never had any arm issues before," Conley said. "I was doing so much work last year in between my starts to be more consistent, to be sharper, to be better. The workload, I think, was too much, and for the first time in my life I had setbacks, and it was my first time on the DL.
"I was immature, I didn't know how to handle it. Then I think I did too much on the DL the first time when I came back I wasn't myself. Just a huge learning curve."
With the frustrations of 2014 behind him, Conley is thankful for the opportunity in front of him.
"There's a lot of players that you see, and players that I've played with, who don't necessarily get the opportunity. That's one of the struggles of baseball," he said. "I feel very blessed and very honored that I have the opportunity here. I'm just going to embrace the opportunity. I'm very grateful that the Marlins ... felt comfortable bringing me up to try and fill that void."