Nakamura, Samaras, McDonald and McGeady scored the goals for Celtic.
Strachan said: “It was sheer determination and ability against people who wanted to work, but unfortunately for them we have more ability than them.
“They gave it their best shot, and we gave it our best shot in terms of how we prepare for the game and how you’re respectful to your opponents.
“When you put that together, then the skill will win and we had more of that, and more pace.
“I thought Barry Robson was tremendous, his energy and his will to win, his enthusiasm.
“He could play in a lot of positions now. He could play on the right, left-back, central midfield.”