"We really had to dig in and did it very well," said Coleman to the club website.
"When we went down to ten men we did what we needed to do - we sat back and were patient and played on the counter-attack.
"I thought Rangers had the better chances in the first half than they did in the second.
"It was a great free kick from Danny to take the lead. He takes all our set-pieces but they have just caught us on the counter-attack after a corner. So I told him if he was going to take a set-piece he should only shoot. I'm glad he did and I'm taking the credit.
"But in the end we were done with a ball over the top. I thought the keeper should have come but he has saved us many times this season and we would have taken that result at half time. The overall performance was very good."
The City boss faces being without striker Leon Best for up to six weeks and Stephen Wright who was sent off and will get a three game ban.