His team needed to win in the Stozice Stadium to claim one of the eight best second-place finishes in qualifying. A late Robert Snodgrass equaliser briefly gave Scotland hope, but a victor did not follow.
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. "You have to ask that question, but you know fine well that I'm going to say I" m the last person I'm thinking about now, ' he said. "All credit to Slovenia - they played well and passed the ball well". Genetically we need to look at things. We are hurting, no one is hurting like the players, it's impossible. "Players, staff, fans, family, I want to make sure they're all right". Not a problem about me.
Should Strachan either walk or be axed a potential appointment of Moyes, who is desperately looking to rejuvenate his managerial career, will continue to be the subject of widespread debate.
England, which was already sure of first place and an automatic berth in the tournament in Russian Federation, beat Lithuania 1-0 to conclude an undefeated campaign with 26 points from a possible 30.
Scotland's drought of reaching a major worldwide tournament will now stretch to at least 22 years after failing to qualify for Russian Federation 2018.
Strachan remained coy on his future, although received support from Celtic striker Griffiths, who expressed hope that the former Coventry, Southampton and Middlesbrough manager would lead Scotland's European Championship qualification campaign. I think we've improved as the campaign's gone on. "Two set pieces have cost us dearly".
Bulgaria 0 France 1
Greece could also finish second in the group as they trail Bosnia-Herzegovina by a point ahead of their trip to Cyprus . Davy Propper, Captain Arjen Robben, and Memphis Depay scored for the Dutch as they beat Belarus 3-1.
"Genetically we are behind", Strachan said.
"They just weren't good enough".
'But you can't change our genetics. Don't know if we can get big women and men together, and see what we can do. "Physically we have a problem against the teams we have faced in the last couple of years".
"But we seem to be able to fight it and battle it with determination, skill and work rate". If you played another player or another system, it might have been a lot worse. "For all the possession they had, they didn't really cut us open".
Gordon Strachan's future as Scotland manager is expected to be decided within a week at a meeting of the Scottish FA board.