Fletcher had only scored one goal in 19 internationals before hitting a treble in Scotland’s 6-1 European Championship qualifying win at Hampden.
And he has also been suffering at club level, having not scored for Sunderland since hitting two against Crystal Palace on November 3.
There was speculation that Strachan might start with Jordan Rhodes against the Group D minnows but the Scotland boss maintained confidence in Fletcher.
“It meant a lot that he stuck with me, but that’s the way he is,” Fletcher told www.uefa.com. “The gaffer’s made a point of standing by the guys who’ve got us to this position and saying that, whatever anyone else says, he knows we’re good players. I’m delighted to have repaid a bit of that faith.”
Fletcher’s only previous international goal came in a 2-1 World Cup qualifying victory over Iceland six years ago but he is now the first Scotland player to score a hat-trick since Colin Stein hit four against Cyprus in 1969.
Fletcher headed Scotland back in front in the 29th minute after Lee Casciaro had stunned the hosts by nodding home a 19th-minute equaliser after finding space round the outside of the home side’s three-man defence.
The former Hibernian forward headed another in the 77th minute and curled home a low finish in the last minute as Scotland - who also scored through two Shaun Maloney penalties and a Steven Naismith strike - maintained their qualifying hopes.
“I feel my game’s about more than goals but you know as a striker that people don’t judge you on how many times you link up play, but on how many you score,” the 28-year-old said.
“So I was conscious of the fact it had been so long. That said, my confidence genuinely hasn’t been dented. You just enjoy these days when they come along, and they don’t come much better than scoring a hat-trick for your country.
“I only realised after the match that I’m the first Scottish player to do that in so long. That was a shock. I wondered if Shaun might get there first, but a few of the lads came up after my second and said: ‘Go on, make sure you get the match ball’.
“You’d have seen from my celebrations how much the goals meant to me, especially the first. That seemed to take an age to go in.”
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