Shaun Maloney's first-half strike deflected in via Akaki Khubutia to hand the Scots a crucial victory, but Strachan was impressed by his side's showing throughout the 90 minutes at Ibrox.
"It was always going to happen at 1-0 against some good players. They threw caution to the wind, but I don't think David [Marshall] had a save," Strachan told Sky Sports News shortly after the game.
"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. It was a manager's dream that first 70 minutes."