Strachan has led Scotland to their most encouraging run of form since McLeish's team just failed at the last hurdle to pip either Italy or France to a Euro 2008 play-off place.
Scotland have lost just once in six games, the defeat coming against highly-rated Belgium, and have kept four clean sheets during that spell.
Walter Smith turned Scotland around following the Berti Vogts era before McLeish took them on a level and the former Aberdeen player is not surprised his close friend and former Pittodrie team-mate Strachan has had a similar impact after Craig Levein's ill-fated reign.
Speaking on a visit to Budweiser's 2013 Clubs Futures programme, McLeish told Press Association Sport: "There is no great secret to it - hard work is something that should just be a given.
"Top clubs like Bayern Munich - you look at them, the champions of Europe and the best club team in the world at the moment arguably, and they have players that are not only exceptional technically and quality-wise. They have fantastic work rate, and Gordon has got a fantastic work ethic out of the lads.
"I have to say, before Gordon came in, I thought that these guys were underachieving. They have been playing in England after all.
"They have been playing in the top division in England, a lot of them - the James Morrisons of this world, playing in the Premier League. I have seen James and the guys, and they are playing at a fantastic level, staying in their teams and most of them first choices.
"Therefore, you wonder why they didn't do better in the early stages (of the World Cup qualifiers). I think there was a confidence factor at Hampden and we were struggling to win games at home.
"Gordon seems to have given them that wee bit of belief now and I think it was just about getting these players to come out of their shells when they were playing in the national jersey. Gordon takes a lot of the credit for that."
- Sports & Recreation
- Craig Levein