The 24-year-old was omitted from the Bhoys' 26-man group, named by Strachan on Monday afternoon, for next month's World Cup qualifying fixtures against Lithuania and Malta.
Six Celtic players made the cut but versatile midfielder McGregor, despite his impressive start to the new campaign, was not among them, leaving Rodgers perplexed.
"I haven't talked to Callum about it but I'm disappointed for him. I don't know what else he can do," he told reporters. "I was surprised when he wasn't in it – then even more surprised when I actually saw the squad. But I don't think he can do any more.
"Gordon and his staff will have their reasons why, I'm just thankful I've got him in my squad. I think about the number of positions he can play and the quality he brings. He's a real special talent.
"Nothing will change with Callum, he'll go on and do what he's been doing over the course of the last 12 months. He'll show how valuable he is for Celtic."
McGregor, expected to be involved in Celtic's Champions League playoff second-leg tie against Astana on Tuesday evening, has yet to earn a full senior cap for the Scotland national side.