Fletcher credited Strachan for making the necessary adjustments in his line-up at half-time of the 5-1 win over minnows Malta in their World Cup qualifier on Sunday.
The Scots were tied at 1-1 at half-time but went on to score four goals in the second half to start their qualifying campaign on a winning note.
"He just calmed us all down and made one or two little tactical changes. They weren't huge, but they really helped the team and the performance. He made sure we were right going back out for the second half.
"I've said before that continuity with the manager is really important and it gives us confidence. That's what makes this campaign a bit different.
"There were positives from the last one, despite the disappointment, and we want to take them forward.
"I think I would agree that a benefit of that continuity was seen at half-time. The manager knows what to say and what to do to get the best from the individuals in the squad.
"A lot of times before with Scotland, we have had changes of manager in different campaigns or managers leaving halfway through and we haven't been able to keep building.
"It's great now because we know what the manager is about and he knows what we are about.
"You are not starting over again from square one, but it's about continuing to work on what has been done before."