Gers made it back-to-back Old Firm victories in a week, thanks to a first-half strike from Ryan Naderi, and the manager praised how his squad dealt with the challenge and the environment at Parkhead.
Speaking to RangersTV at full-time, he said: “The question was asked of us if we could back it up from last week, and I am absolutely delighted that we managed to do that.
“We knew it would take a big performance, a different set of circumstances obviously, with no supporters, but we had to get off to a strong start. I didn't think we were great the first 10/15 minutes, but I thought once we managed to get a grip of the game, we looked a real threat, and we thoroughly deserved to go in front at half-time
“It was then a case of trying to maintain the levels, knowing that Celtic would maybe change as they did in terms of personnel.
"It is a good reference point again that you can say you dealt with it and dealt with it really well.
“I was really pleased with the performance, and I am delighted that although there were no fans in here, I really hope they enjoy their Sunday because we know who we play for and we know how many people will take pleasure in that.”
On the defensive display, with a fourth clean sheet in a row, McInnes added: “I think it gives us a platform; we have got good players back there, good pace, good aggression, good ability on the ball. Penrice, Sterling, Makhanya and Fernandez have been a mainstay of that, but you have people like Ben Godfrey to call upon, Ross McCrorie, you've got others that can come in, so the squad.
“Celtic have only had two shots on target in the two games, and that doesn't just come down to a back four and a goalkeeper; that comes down to the work ahead of it and from Kevin and Ryan at the top, all the way back to Ivor. I think it shows how each department is working hard for the team and the club.”
"I think he takes a bit of comfort from having Kevin up there; you have got Bojan ready to come on, and obviously there was a lot made of losing Youssef and losing Lawrence. It is great to have these boys deliver such a big performance on a big day.
“It is only three points, but in the context of the season it was important for loads of reasons not to let Celtic open up that gap even more. We have work to do, but we'll take the good from it, and to get back-to-back wins against Celtic you need to do a lot right, so we are really pleased with what the lads are giving us.”