Celtic defender Mulgrew has only just returned from a long injury spell, but Strachan believes that the 29-year-old’s mere presence in the team makes them stronger.
“He was a huge asset for us when we played the Republic last time – and I mean huge,” the 58-year-old told The Sun.
“I thought he had a terrific game and just having Charlie in the squad makes us stronger. Not just in midfield but in other positions too."
“Charlie has been back in the Celtic side and they would not have put him in if he was not right.”
Mulgrew made his first competitive appearance for Celtic since December 2014 on Friday, when he came on as a half-time substitute for defender Jason Denayer in the Scottish Premiership clash against St. Johnstone away from home.
The former Aberdeen star played for the entire second half of the contest at McDiarmid Park in Perth.
The Scot gave a good account of himself in the match, which ended in a goalless draw, although at times he did look a bit rusty (for obvious reasons).
Mulgrew is a versatile player who is able to feature as a central midfielder, a central defender or a left-back.