Captain Lawrence Shankland scored from the penalty spot midway through the second-half to see Gers over the line at Pittodrie.
Speaking to RangersTV at full-time, he said: “I am proud of the players, the contrast in how we feel from Thursday is night and day.
“I used to be in that away end as a fan, and I always wanted to experience that as a manager, winning here, and I thought the fans were brilliant throughout.
“There has been a lot of anxiety, anger and frustration since Thursday’s performance, and it wasn’t a nice place to be in. We were in a tough spot but I think the players responded brilliantly.
“After playing 120 minutes, the physical output was incredible from the players, and the togetherness of the squad is clear to see. For the first time I thought it was a complete 90 minute performance. We have had little moments of enjoyment, but I felt today we had a clean sheet in us, and I think we looked a threat,
“I don’t think we had a poor performance today and when you come to Aberdeen it is not always quality that wins the games here, but you need to be competitive, you need to be together, and I thought we were that.
“It just took a bit long to get the first goal but I'm glad we have managed to win a game that we thoroughly deserved. We would've taken any sort of win today but to win it with a strong performance is even better.”
On debutant Minsu, McInnes continued: “It is difficult for him to come in when he's only had one day training with us. We trained yesterday in Aberdeen and there was just enough in that training session for me that made my mind up.
“He was sharp, he was eager and he's got quality. I think when you get those ball carriers, with that quality and speed in the team with Gassama, Curtis and Minsu I thought it allowed defenders just to be defenders.
“You don't have to do too much more than just defend your area and get your clean sheet, midfield has to be competitive, land on the ball, get the players who can go and make the difference.
“I think that added speed helped Lawrence have a better game as well and it was a brilliant moment for him scoring, it wasn't easy in front of the Aberdeen end to go and stick that away, so having that experience to go and deal with that was great as well.
“I think we need to make small steps, that was a good step, and Falkirk away is another tough game so we need to do a lot of what we did between Thursday and today in terms of that physical output.
“We'll look at how the lads are in terms of their fitness, but we hopefully take the good from the game today and we try and do all we can and if we can just start getting a bit of consistency of performance then the results will come.”
MYGERS: From priority access and behind-the-scenes opportunities to special events and unique moments, MyGers brings you closer to the action on and off the pitch
RANGERS MUSEUM AND STADIUM TOURS: Experience the magic of Ibrox Stadium, with your very own ‘access all areas’ pass