Rovers overcame the shock of going behind inside 60 seconds to take a second half lead thanks to goals from Jordan Rhodes and Nuno Gomes, and although the home side twice pegged Rovers back, injury time strikes from Scott Dann and a second from Rhodes ensured a first away win of the season.
The Rovers boss was delighted with the goals his side scored, but not with the defending as they allowed City back into a game on two occasions.
"I must say at times I thought we had the points in the bag but then we go and have a bit of a mistake," said the Scotsman.
"But the mistakes are to be analysed another day, I think the big positive from today was from going a goal behind we showed good courage to then dictate the rest of the half, to continue to keep passing the ball and make the chances.
"Fundamentally that is the way we want to play and I thought the victory was well-deserved even though it was hard to come by at times.
"I thought the performance was good, I don't think our defending as a team was great, just like at Leeds, to concede six goals away from home in those two games was poor, but four points from those two games is excellent.
"Today we'll enjoy going top of the league and we'll enjoy getting three points on the road."
subscribers will be able to watch extended highlights of the game online on Monday.