The Scottish national team will face Peru next Tuesday and Mexico the following week with McLeish having released the squad-list in an attempt to satisfy club managers, yet has seen many of his key players pull out.
Shortly after the announcement, Rangers' Allan McGregor, Newcastle's Matt Ritchie, Bournemouth's Ryan Fraser and Wolves' Barry Douglas were forced to withdraw with medical issues.
On Tuesday, they were joined by Celtic midfielder Armstrong and Hearts defender Souttar, forcing the Scotland boss to draft in additional recruits for the international friendlies.
McLeish admitted: ''It is getting quite thin. We need to look for a couple of replacements. The guys going there will need to do giant-killing acts in South America.''
''Stuart has a little tweak in his hamstring. He flagged it up right away after the game [Celtic's Scottish Cup victory]. I believe it has been scanned. He genuinely wanted to come. You have to hope everyone else genuinely wanted to come to play for their country and enhance their careers.''
''It is not to be. It is a shame to lose him - a very experienced guy and a tremendous player. But we are looking forward to the overall grand scheme of things.''
McLeish added: ''We have made some concessions and that kind of thing but the late call-offs were disappointing but I am not blaming the players. We have some great players out there and we want them to be ready and available to play for Scotland.''