Substitute Johnny Heitinga drilled home an injury-time winner after Steven Pienaar's first-half opener had been cancelled out by Marvin Sordell for the npower Championship strugglers.
Moyes said: "It is good to put my best teams out but that might run aground later on if we are running out of legs or we get injured.
"There were times I was looking over my shoulder and I didn't have a lot of options.
"I thought in the second half we had most of the play without being that creative, but we looked the more likely to score.
"It was great to get the job done. I've had many years of not getting through in ties quite similar to this."