Before his £10m move to Russia two years ago, the former Hoops star had been on the wrong end of many disappointing Champions League results with Celtic.
He did his best to ensure Spartak would not be the first club to fall to them on the road, but accepted the final result.
McGeady said: "Overall we didn't really get going. Celtic went one up on the break, and that killed us a little bit.But then we got back into the game and got in front."
Even at 2-1, McGeady was always wary of a Celtic come-back, and believes that the red card shown to defender Juan Insaurralde with 28 minutes remaining was the turning point.
McGeady, who was replaced for the last 15 minutes, added: "The sending off changed things.
"Celtic played well on the counter attack and probably overall deserved the victory."