A Shunsuke Nakamura free-kick nine minutes from time gave the Glasgow giants a dramatic victory over Manchester United at Celtic Park. And with one game remaining in Group F, the Parkhead side have nine points and cannot be stopped from entering the last 16 by either United or Benfica, who play each other next at Old Trafford.
The visitors dominated the first half but in the 81st minute the home side took a sensational lead when the Japan international curled a wonderful free-kick past goalkeeper Edwin van der Sar. More drama was to follow.
The visitors missed a last-minute penalty when Artur Boruc saved Louis Saha's effort. Afterwards a drained Strachan said: "I don't believe it. There must be a rule that says we don't go through.
"I will wake up tomorrow and find someone has scored an extra goal against us somewhere. "I better check Teletext tomorrow to make sure. "It was 15 minutes before someone told me and 20 minutes before I took it in.
"But when you see the fans, the people in the directors' box and behind the scenes, it's priceless."
The Celtic boss acknowledged his side had been given a first-half lesson by the Old Trafford who weaved some impressive patterns – albeit without providing Boruc with any real threat. However, Strachan helped stem the tide when he introduced Jiri Jarosik and Shaun Maloney for Evander Sno and Maciej Zurawski at the interval, and thereafter the home side looked slightly less edgy if no more of a threat until Nakamura popped up with his piece of magic.
Strachan said: "I would only give us a five out of 10 for that performance. "In the first half we weren't that great and we had some square pegs in round holes. I just hope people forget that first half and remember the second.
"I didn't think we could play that badly. "We weren't passing, we weren't confident and had no presence so I had to make changes.
"We weren't at our best and couldn't get our system going. "But I was lucky that I had the players to change it around. "And what we have achieved is all down to the players. "And I knew if we kept Nakamura on we would have a chance."