"That was like a cup tie; it was nervy," Strachan told BBC Scotland.
"It was intense for people to watch. Either team could have won it, but we had the luck today."
The fiery Scot also insists that he has no plans to alter Celtic's playing style, despite being disappointed by his side's play during the first half.
"We will continue to try to play football while winning at the same time," he insisted.
"(Shunsuke) Nakamura got mugged for the first fifteen minutes of the game, but he produced a cross (for Scott McDonald's goal) just when we needed it.
"We had to try to get the ball into areas where their defenders had to defend. We did that, whereas before I felt their midfielders were doing the defending."
Celtic are now eight points clear at the top of the SPL, but Strachan was cool on what the win meant for his side's season.
"It doesn't put pressure on Rangers, it just takes the pressure off us for awhile.
"We can just look forward to the next game. Whatever happens happens."