The Scotland international underwent a knee operation during the summer and has only just returned to light training.
An exact date as to when Morrison will be able to return to West Brom's midfield is unknown and the new boss feels that he may struggle to adequately replace the 28-year-old.
"It's a big concern that Morrison hasn't trained all summer," Irvine told the club's official website. "He's an important player for us and we could have done with him being with us for pre-season.
"Unfortunately he had an operation just before pre-season started and sadly it's taken him an awful lot longer to get back than was anticipated.
"It's a big disappointment because we could do with all our best players being fit and available. Clearly, when you miss a pre-season, it becomes difficult to catch up.
"He joined in the early part of training on Friday and then went away and did his own work. The boys that have done pre-season have been in for five-and-a-half weeks and there isn't a short-cut to getting fit and ready for games.
"He's a fit lad, which is a real bonus, but it's going to be a big, big task for him to get up to his maximum and best condition."