The Tartan Army are officially out of the running to reach Brazil, rock bottom of Group A after two goals from Filip Djuricic condemned them to defeat in Novi Sad.
Reminiscent of their loss to Wales at Hampden Park on Friday, the Scots surrendered a good position in the game by conceding two goals in quick succession and Strachan believes that it is defensive frailties which are damaging his side's ability to compete.
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"The same thing happened on Friday so, if we lose a goal, we really need to see that the game's not finished. There's a time in international football the players have to be told.
"It's a shame for everyone who makes a mistake after putting a lot of good work in. It's not dishonest mistakes.
"It was heavy going and I thought technically they were a right good side. Physically they were stronger than us which gave us problems but they didn't have bigger hearts than us.
"Some of these lads have never played international football before and some of them are playing with injuries but they took the responsibility on their shoulders.
"The longer the game went on, the better it got for us. We were happy with loads of things but it happens too often that one goal goes in and another one quickly follows so we have to remedy that.
"It's easy to work on people who are good people. It's not a quick fix to get as strong and as technically gifted as that but there are lots of things I know I can work on."