Carter, who played under Irvine at Preston, believes that the 55-year-old has the right credentials to succeed at The Hawthorns.
"I understand the frustration of the supporters because it's a surprise appointment," he told the Express & Star.
"Alan is probably the most dedicated coach or manager I have ever worked with. The way he goes about his work, the way he plans his sessions and the way he prepares his teams for games is outstanding.
"He is the most thorough manager I have ever played for and I know that the players at West Brom will enjoy playing for him. He is a manager who will want his team to play football."
Irvine has most recently been working as academy manager at Everton.