Jonathan Walters gave Ireland the lead at the Aviva Stadium but a John O’Shea own goal earned the Scots a potentially vital point.
The result maintains their two-point advantage over Ireland and keeps them in contention to qualify automatically for Euro 2016.
“We are still in with a good chance of qualifying,” Strachan told Sky Sports. “And after the amount of games we have played, to have a good chance is terrific from the lads.”
Strachan added he expects “a few twists and turns” in Group D but praised his side’s battling display against Ireland.
“After our first-half performance, which could have been better, we were decent in the second half,” he said.
“I was happy in the second half when the game died down and we had some good possession and frustrated them. The goal right after half-time gave us a huge boost.”
Scotland were perhaps unfortunate to fall behind in the 38th minute as Walters appeared to be offside when he finished from close range.
But Strachan refused to blame the referee for not disallowing it, saying: “Some of the refereeing was magnificent, we can all make mistake and I am not sure if it is. It’s June, I don’t care now.”