Dave Mackay’s deflected goal on the hour-mark was enough for the Perth club to grab maximum points from the Hoops for the first time in 18 attempts in all competitions, dating back to April 1999.
Former Rangers and Dundee United midfielder McInnes said it was a great day for St Johnstone whilst heaping praise on goalkeeper Peter Enckelman for his overall performance which was highlighted by a penalty save from Kris Commons in just the third minute.
"We have to enjoy today,” McInnes said at after the match.
"I have left here with my tail between my legs often enough as a player and as a manager in the past.
"I think we had a more experienced team than Celtic and it is not often you can say that when you play against the Old Firm.
"I thought the penalty was harsh but we are lucky to have Peter Enckelman, he has been a different class for us."