Strachan's side got their first win of Euro 2016 qualifying Group D at Ibrox after Akaki Khubutia's first-half own goal proved decisive.
Building on their strong showing in September's 2-1 defeat to world champions Germany, Scotland showed flashes of their quality - even if they lacked a finishing touch on occasions.
However, Strachan felt his side were always in control even when the visitors went in search of an equaliser late on, with substitute Irakli Dzaria firing wide from the edge of the area.
"It was always going to happen at 1-0 against some good players [that] they threw caution to the wind. But I don't think David [Marshall] had a save," he told Sky Sports.
"They had a chance towards the end but they put it wide because we had two guys putting our bodies on the line.
"To get a great performance like that is fantastic because after losing the first game there is pressure on you. Whether it's Germany or not, the pressure is on.
"But to play that way is absolutely outstanding. If you were to say to me we're going to get that many chances against a good Georgian side...it was a manager's dream that first 70 minutes."
