A 2-2 draw away to Slovenia on Sunday evening cost Scotland the chance of progressing through to a two-legged tie next month, seeing their agonising wait for a place in a summer competition go on.
Strachan believes that a lack of height in the squad is possibly to blame for this latest failure, but he is more than happy with the desire shown by his players in the second half of the campaign.
"Genetically, we're behind. The last campaign we were the second smallest, apart from Spain, so that means we had to pick a team tonight to try and combat the height and strength," he told reporters. "Even at that we couldn't combat their height and strength at set plays.
"Genetically, we have to work at things. Don't know if we can get big women and men together, and see what we can do. It is a problem for us because we have to fight harder for every ball and jump higher. Nobody tell me their technique apart from one player is better than any of ours but physically we have a problem.
"But we seem to be able to fight it and battle it with determination, skill and work rate. That takes a lot out of you and that's what's happened tonight. These guys have put so much into this, that I really do feel for them."
Scotland finished third in Group F, level on points with Slovakia but with an inferior goal difference across the 10 matches.