Strachan has been Scotland head coach since January 2013
Gordon Strachan lamented Scotland's lack of physical stature after missing a World Cup play-off place.
Victory in Slovenia would have guaranteed a play-off but a painful 2-2 draw allowed Slovakia to overtake Scotland on goal difference.
"Genetically, we are behind," said head coach Strachan.
"We had to pick a team to combat their height and strength. It's a problem for us because we have to work harder for every ball."
Strachan, 60, refused to be drawn on his own future, saying it was "an honour to work with this group".
"The players are hurting badly but when they look back they can be proud, they gave it a right good shot.
"They left nothing in the dressing room, over the last two games especially.
"We've been beaten on goal difference by Slovakia, who are an excellent side."
Scotland had four points after four games, following a calamitous home draw with Lithuania and heavy defeats away to Slovakia and England.
Strachan's side finished with a six-game unbeaten run, including four victories, but it was not enough to get the runners-up place behind runaway Group F winners England.
Leigh Griffiths shot Scotland into a first-half lead but the visitors endured a wretched period after the interval as substitute Roman Bezjak scored twice.
Robert Snodgrass found a late leveller after Darren Fletcher had spurned a wonderful chance in front of goal but it was not enough as Slovakia cruised to an expected home win over Malta.
Griffiths opened the scoring for Scotland but the visitors could not find the win they needed
"We couldn't combat their height and strength at set-plays," added Strachan, with Bezjak's goals coming from a free-kick and a corner.
"Nobody can tell me that, apart from one player, they are technically better than our players. But, physically, we have a problem.
"We can fight it, battle it and get through games on sheer determination and work rate and that takes a lot out of you.
"That's what happened tonight. These guys have put so much into this. I really feel for them but they can also be really pleased.
"This group is as good as anything I've worked with."
'No one hurts like the players'
Former Celtic and Middlesbrough boss Strachan, who has been in charge since January 2013, took a now familiar line when asked about his own future.
"No one is hurting like the players, it's impossible," he said.
"The fans can't hurt like that, I can't hurt. There shouldn't be any talk about what I'm thinking or what I'm doing at this moment in time because I am just looking after them.
"Sometimes in life you have to hurt badly before you achieve things.
"I have been lucky enough to achieve things with other groups of lads but these have achieved as much as anybody.
"I have never been in a dressing room as silent as that. That was a real hurting silence. I really have to thank them for the effort they have put in."
Source: bbc.com