Two set-piece goals from Roman Bezjak overturned a first-half strike from Leigh Griffiths, and Robert Snodgrass could not convert a headed half-chance in the dying seconds after he had levelled with two minutes remaining.
Bezjak's movement allowed him a free header from a Josip Ilicic free-kick and he had yards of space to slot home from 12 yards following a corner from the same player.
Strachan refused to discuss his own future after Scotland missed out on second place in Group F to Slovakia, who beat Malta 3-0. And he declared himself honoured to work with a group of players who he feels are battling against the odds.
The likes of Ikechi Anya, Griffiths, Andy Robertson, Kieran Tierney and Barry Bannan were up against bigger opponents and Strachan claimed that had taken its toll, at the Stozice Stadium in Ljubljana and elsewhere.
Scotland's head coach Gordon Strachan looks on after the FIFA World Cup 2018 qualification football match between Slovenia and Scotland at the Stadium Stozice in Ljubljana, Slovenia on October 8, 2017. / AFP PHOTO / Jure Makovec (Photo credit should read
Image credit: Getty Images
"Genetically we are behind," he said. "In the last campaign we were the second smallest, apart from Spain.
"We had to pick a team to combat the height and strength at set-plays. Genetically we have to work at things, maybe we get big women and men together and see what we can do.
"But it is a problem for us because we have to fight harder for every ball and jump higher than anyone else.
"Nobody can tell me their technique, apart from one player, is better than any of ours. But physically we have a problem. We seem to be able to battle it and get through just with sheer determination and skill and work-rate. And that takes a lot out of you."
Players of national football team of Scotland look dejected after the FIFA 2018 World Cup Qualifier match between Slovenia and Scotland at stadium Stozice on October 08, 2017 in Ljubljana, Slovenia
Image credit: Getty Images
Scotland were unbeaten in their final six qualifiers, but ultimately could not make up for an indifferent start, with a home draw against Lithuania arguably the most damaging result.
Strachan said: "Over the 90 minutes and the last year, it's been an honour to work with these guys. At this moment it's obviously disappointment, but my disappointment is nothing compared to the players'.
"When you see them at the end of the game, I don't think I have seen a group of players that exhausted and disappointed.
"As I said to them, you can go away and be really proud of yourselves because you pushed yourselves to places some maybe didn't think they could go, because we were against a physically stronger side, a side that has never conceded a goal here.
"Against a physical side, we knew set-plays would be a problem and they scored from two set-plays. We can't change genetics and just can't play the biggest people in Scotland.
"Technically we are fine, but our lads have got to work harder on the ball than bigger lads who are 6ft 2in or 6ft 3in."
Slovenia's players celebrate after scoring a goal during the FIFA World Cup 2018 qualifier football match between Slovenia and Scotland at the Stozice stadium in Ljubljana, on October 8, 2017
Image credit: Getty Images
The former Celtic boss added: "They have done fantastically well. It's an honour to be their coach.
"I have been successful with other teams and, with all due respect to all those lads, and they will know who I am talking about because they are my mates now, this group is as good as anything I have worked with.
"This group do it for nothing, they come and do it for the country and their families and the fans. They are hurting badly.
"They gave it a right good shot and left nothing in the dressing room. We have just been beaten on goal difference by Slovakia, who are excellent, and that was a right good side tonight."
Slovenia boss Srecko Katanec said: "I'd like to congratulate my boys. We were clearly the better team for the whole game."
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