The D-backs left-hander, who was out of Minor League options, had an impressive spring, and it was widely assumed if he did not make the team, he would be claimed on waivers by another team before he could be sent to the Minors.
Zagurski, however, did clear waivers and began the season for Triple-A Reno.
"It just didn't work out at the time, but I went down there for a couple weeks and was fortunate enough to get back and hopefully will be here for a long time," Zagurski said.
Rather than pout about his situation, Zagurski continued to pitch well, compiling a 2.00 ERA in six games for Reno before being called up to replace left-hander Joe Paterson last week.
In his lone outing heading into Sunday, Zagurski allowed one run -- a homer -- in two innings.
"I think it's a constant battle to try and get better every day," Zagurski said. "I thought I had a pretty decent spring, and going down to Reno, I felt like I threw the ball even better in Reno than I did during the spring. I felt OK about my outing the other day. One bad pitch. I didn't execute great, but I got through it for the most part and it's something to build on."