The uncapped Celtic man had been tipped to earn a place in Strachan’s squad for the crucial World Cup qualifiers against Lithuania and Malta, but was again left out in favour of familiar faces.
Stracham opted instead to hand recalls to Premier League duo Matt Ritchie and Matt Phillips in the 27-man squad set to travel to Vilnius before hosting Malta as they look to close the four-point gap to second-placed Slovakia in Group F.
After deciding not to hand a maiden call-up to the in-form McGregor, Strachan said: “A lot were close. Looking at the midfield and the squad, there are a lot of good, good players in there, who have done well for us over the years and we can rely on.”
Steven Whittaker has also won a recall after last appearing for the national side in 2016, while Millwall goalkeeper Jordan Archer has earned a first call-up and regular James Morrison misses out through injury.
John McGinn and Steven Fletcher also return with Robert Snodgrass and Grant Hanley included despite not playing a minute of first-team football so far this season.
Strachan admitted it was not ideal to have so many players out of action.
“There’s a few,” he said. “That’s why the squad is probably larger than normal.
“One or two are playing knocks and may need a rest and one or two who aren’t in the team at the moment, so we made the squad a wee bit larger.
“We will keep an eye on them, and their fitness and monitor the guys with knocks.”
However Strachan was optimistic over his squad, and suggested the impressive performances of Celtic in Europe were crucial to improving the fortunes of his side.
Brendan Rodgers’ Hoops have one foot in the group stages of the Champions League after beating Astana 5-0 in the play-off first leg last week, and Strachan said European football was crucial to the development of Scottish players.
“It’s a huge thing, playing regular Champions League football,” he said. “You go back 10 years to when Rangers and Celtic were playing regular European football - the clubs were sending about 10 players to the squads, playing regular European football.
“It’s a huge, huge difference. It’s a great learning curve in how to deal with big matches and atmosphere. It makes a big difference.”
With Scotland due to face second and third-placed Slovakia and Slovenia respectively in October, they must put themselves in a position where they can still finish in the top two and Strachan will not be holding back.
“We have got to try and win both games and that’s what we set out to do,” he said. “We never set out to draw a game, we set out to win and if we draw, we draw.
“Whether it’s Germany away, or down at England, we set up that way.
“I don’t think we have the physical capabilities at the back to take long periods of being under intense pressure.”