After college he got his first job as the freshman coach at Texas Western under Don Haskins. He was at Texas Western until 1966. After the '66 season, Moe was hired to coach Memphis State University replacing Dean Ehlers. A great recruiter, he recruited Larry Finch and Ronnie Robinson, two local Memphis legends to come to Memphis State. He was, however, let go after a 6-20 season in '69-'70 and never got to coach them on a collegiate level, but left his mark on the city when Gene Bartow took those recruits and added a few others and went to the NCAA finals in 1973. After leaving Memphis State, Moe got a position as an assistant coach at Nebraska and stayed in that position for 8 years. He was named acting head coach when Joe Cipriano became ill with cancer. He replaced Cipriano in 1980 and was head coach at Nebraska until 1986. Iba's teams there achieved 3 NITs and one NCAA bid, the only NCAA appearance in the school's history to that date. He was an assistant at Drake in 1986-1987 and was then hired at the head coach at TCU where he stayed until 1994.