The former Celtic boss said that he is proud of his squad for their efforts in recent World Cup qualifiers, despite managing only one point from their last two games.
"At this moment in time, the people I feel sorry for are the players. They have put so much work into the last two games. As a group, I'm really proud of them," he told BBC Sport following the Slovakia reverse.
"The second group you feel sorry for are the supporters who have come here tonight. I'm not thinking about myself."
Strachan went on to say that Scotland still have a strong chance of qualifying for the finals, lying just three points off the top of Group F after three matches, despite winning just one of their games.
"We'd like to be better off but we are one point off a playoff place and I've said before that it's a crazy group," he added. "Form can change in a couple of weeks and this campaign is over a year."
Scotland's next competitive match is away to England at Wembley Stadium.