Young was a threat all evening in poor weather conditions, with both sides even leaving the pitch at one point due to a hail storm.
The game resumed, however, and Young gave United the lead midway through the second half, powering home from outside the area after linking up with substitute Chicharito.
“I have spoken to Ashley. I told him to make sure you do everything right and get on with it," Moyes told reporters. "He got kicked a few times and went down and got back up.“He has also got the ability to score, he is good in training and he needed the goal as well."
Young has come in for criticism this season for below-par performances and accusations of persistent diving and Moyes warned the Englishmen he must continue to produce in order to stay in the first team.
“We have a lot of talent in wide areas to select from. You need to score and play well if you want regular outings," he added.
“He has got to keep stepping up like he did, when you are in and you get an opportunity you have got to show.”
The Red Devils will now face Sunderland in the semi-finals, with local rivals Manchester City set to face West Ham in the other half of the draw.