Strachan looked like winning his first competitive game in charge when Grant Hanley headed the Scots in front seconds before half-time, but they imploded in two second-half minutes to continue a woeful run of form in Group A and all-but end their slim chances of going to Brazil next summer.
Norwich midfielder Robert Snodgrass was sent off for a second yellow with 20 minutes to go, giving away a penalty which Aaron Ramsey converted, and less than two minutes later Hal Robson-Kanu headed what turned out to be the winning goal.
Strachan said: "We tried to overplay, plus our passing wasn't good enough in the first 25 minutes.
"Once we got to grips with that we got near the goal, we threatened, then we scored and the start of the second half was terrific, everything we were hoping for. Making chances, hitting the post, and we might have had a penalty.
"At international level you've got to take your chances when they come along and we didn't.
"Then we go down to 10-men and that was a problem for us. We decided to gamble near the end, try and play a 3-4-2, but we didn't have enough time to do that. They kept possession of the ball well at that point so there's a lot of things to learn."
Strachan also revealed his concern over the ankle injury Sunderland striker Steven Fletcher suffered early in the match - he was carried off and has no chance of playing in Tuesday's clash with Croatia.
He added: "Steven is getting assessed at this moment and obviously he's not going to be fit to play on Tuesday.
"We're worried for him but hopefully it's not as bad as it looks. He'll now go back to his club and get assessed there so we wish him a quick recovery."