Morrison was not risked for the midweek FA Cup replay defeat at Burnley but returned for Saturday's 3-2 Barclays Premier League reversal at home to Newcastle.
"We wanted to strengthen his problem areas rather than send him away where he's out of our control," Mowbray told his club's official website.
"We want to control his rehabilitation."
Morrison's withdrawal is welcome news for Mowbray, who this week lost Chris Brunt, Dean Kiely, Robert Koren, Marek Cech and Abdoulaye Meite to international call-ups, while on Tuesday striker Roman Bednar was an 11th-hour inclusion in the Czech Republic squad for Wednesday's friendly with Morocco in Casablanca.
"Roman's been called up," Mowbray continued. "He's flying to Casablanca – it's a bit warmer there. Nobody else has pulled out.
"In an ideal world, we'd like them all to stay with us, rebuild their confidence and work with them during training because we have some important games coming up.
"Every manager is the same but you're governed by rules and regulations about call-ups."