Nico Raskin, Mohamed Diomande and Hamza Igamane got the goals for Barry Ferguson’s men in what was the first victory at Parkhead in five years.
Speaking exclusively to RangersTV at full-time, he said: “It was a big one, especially after this week and the Fenerbahce game as well. It is the first time since I have been here that we have come and beat them, so it is a great feeling and we had the fans back as well to give us that extra boost.
“We watched them, and we thought let’s try something different, we were more aggressive, and they didn’t like that and we went two goals up.
I think you could see the legs were getting tired doing 120 minutes during the week, but we dug deep, let the subs come on and do their thing and then Hamza got the winner with a great goal.
“The gaffer has rattled it into us that we have to play for each other, run for each other, if someone makes a mistake someone else will be there to mop it up and I think you could see that everyone put in a shift.”
Sterling was involved in a huge moment in the first-half as he got a vital interception on a header from Maeda to deny the Celtic man a goal.
On the clearance, he said: “I was just doing my job, I saw it coming over and I thought let me get something on it and thankfully it went out of the goal and not in it but I was just playing my part. Everyone has got a role to play and I'm just doing mine.
“I am still coming back from injury, so I have still been managing my minutes a bit but for me I think the gaffer has got the belief in the changing room, he is right behind us, his coaching staff are right behind us and it is just him bringing the best out of us.
“We know that we have messed up in the league, but it is good to get the win and hopefully we can continue in that direction for the rest of the season.”