McGeady helped himself to what proved to be the only goal of the game shortly before half-time, as Celtic held on for three precious points.
The Scottish champions headed into the match at Parkhead bottom of Group D, following a 1-0 defeat to Benfica in Lisbon a fortnight ago.
But, thanks to McGeady's strike, Celtic have now breathed new life into their European campaign and Strachan had nothing but praise for the man who made all the difference tonight.
"Along with his technical ability, his physical ability is fantastic. He is now using that God-given talent that he has and he is enhancing it, which is great for him and first class for us.
"I love people enjoying themselves and he is enjoying himself at the minute but he is enjoying himself for us, not for him. Even when he doesn't have the ball, he is a good team-mate."
Asked about his assessment of the group - and Celtic's chances of progressing to the knockout phase - Strachan added: "It's good fun. We are still there.
"I said before the game that I was happy with the performances so far and I still am."
"Physically and mentally we weren't at our best in the first half," he said.
"In the second half we were stronger. I thought we were excellent and for a spell we could have scored two or three goals."