The reason he was at Hampden was to discuss his squad for next month's World Cup double-header against Belgium and Macedonia. Guess what? There there were more questions about one missing name than the 27 on his list combined. Strachan delivered an extended tribute to Kenny Miller's Scotland career on the day that the player announced his retirement from international duty.
Miller's first cap came in Poland in April, 2001, and his last at Wembley nine days ago. Over those 12 years there were no tournament finals but 69 appearances and 18 goals including memorable strikes against Germany, Italy, Ukraine and, vivid in the memory, England. He offered tireless running and patience, often ploughing a lone furrow and playing with only isolation and frustration for company. He buzzed defenders and pressurised them. He scored poacher's goals and sometimes instinctive, explosive ones. His commitment was evident in his unquestioning willingness to be recruited even when that meant making long journeys from Turkey or Canada in the hope of getting some game time in low-key friendlies. He would go for sequences without a goal for his country, sometimes long ones, and then pop up with something vital.
There were forgettable moments too and enough botched, one-on-one chances to exasperate a sizeable chunk of the support. His departure will ventilate the Scotland attack and was not mourned by all fans yesterday. Team-mates and managers took another view. Miller was picked by Craig Brown, Berti Vogts, Walter Smith, Alex McLeish, George Burley, Craig Levein and finally Strachan.
Only last week, after Wembley, Strachan had speculated that there was plenty more to come from the 33-year-old in Scotland's cause even as the player himself was hinting that his tour of duty was coming to an end. They spoke this week and Miller confirmed his mind was made up. The national team must look elsewhere. Strachan didn't quite describe him as irreplaceable but he didn't stop far short. Could anyone else do his role? "At the moment no. But it can be done over time, that's for sure." Leigh Griffiths, Jamie Mackie, Shaun Maloney, Ross McCormack and Jordan Rhodes were listed as the forwards for the two imminent games - Steven Fletcher remains unavailable through injury - and that handful of strikers has scored only eight times in 59 international appearances.
It was no surprise to learn that Strachan briefly attempted to talk Miller out of his decision to retire and dedicate himself fully to his club side, Vancouver Whitecaps in Canada. "I did for about a minute but then I thought to myself, 'this is really selfish'," said Strachan. "I told him he'd have to excuse me because I went into a kind of selfish mode trying to change his mind. I suddenly thought it was wrong and I shouldn't be doing it. He'd done as much as he can. I'm thinking about myself here, he has to think about his own career. The decision was difficult enough for him as it was and I was actually making it harder so I had to say to myself, 'shut up Gordon'.
"Kenny was saying Vancouver had invested a lot in him, not just financially but in terms of trust. He feels he has to give something back to them. The onus is on him as a marquee player to do the best he can."
At club level Miller played for Hibernian, Rangers, Wolves, Celtic, Derby County, Rangers again, Bursaspor and Cardiff City before moving to Vancouver. His club career carries on. There was a Parkhead tribute to him yesterday from his former team-mate, Neil Lennon.
"I played with him and he sacrificed a lot for the team," said Lennon. "He's one of the hardest-working players that I have played with and a really good team player. I think there is no better way to retire by scoring a 'worldie' at Wembley against England. I suppose the timing is strange but with the travelling back and forward from Canada that he's doing now, it must be taking its toll on him."
Strachan spoke with the sort of enthusiasm and respect he reserves for those professionals he truly admires. He did not overpraise Miller and he put his talent into a sensible perspective, but there was no disguising the sense that he could do without losing him so soon after Kris Commons made himself unavailable. Like Strachan himself, Miller had extended his international career by looking after himself.
"Kenny can leave with no regrets. He's given it everything. He's not as talented as Kenny Dalglish, Brian McClair or Charlie Nicholas, people like them, but nobody has put in as much work as he has, that's for sure. He doesn't just run about. If you look at the goals there are some good goals in there as well. He got better as he got older. He showed there the other night with the hard work he's put in that he knows what made Kenny Miller a good player. When he was younger he might have thought 'can I do this, can I do that?' Then he realised 'I can't do this or that, I'll stick to what I'm good at and make my living this way'.
"He was a strong-minded character. I wouldn't want to put him up on a pedestal, but what I'm saying is he got the most he could from his ability."