Goalscorer Harry Darling shared his immediate post-match reaction saying: "it was a really, really, good week. It was important for us.
“We said after the Derby game, obviously we went to back it up again and we wanted to really win this game before the international break.
It was a really good performance.
“It's enjoyable, to be honest.
“I'm a bit more buzzing about the clean sheets.
“I think we haven't been good enough, especially at the start of the season with goals and to get back-to-back clean sheets was another really big goal for us today.”
Norwich’s win today sees them with four wins a row, turning around a disappointing run of results.
“I think that it was frustrating as well because on the back of last year we know how good we can be and obviously we didn't show that at the start of the season.
“We know that as players we weren't good enough, it was as simple as that.
“It's nice to get back to where we were a little bit and we just want to keep pushing on it.”
City were 5-0 up during stoppage time when Bristol has a glimmer of goal, but Darling made a vital clearance off the line.
“I think it was probably my mistake at the start. It was a good clearance.
“I should have stopped it first, but like you say, we wanted to keep the clean sheet today, and it's important to do that.
"I think if you look at the whole game, I think we made some really good blocks.
"They had a couple of shots on goal and we made some good blocks, and you know, we defend from the front.
“The boys press really well at times, and you know, it's a whole effort. It's not just a defensive unit, it's a whole team.
“We want to keep improving on that and keep going through as well."
Harry expressed his happiness with scoring but is keen to push for more.
“Yeah, I’m really happy. I probably should have had another one, but yeah, really happy.
“I had a lot of time to think about it, so just wanted to place it.
“It wasn't bad, but I'm just happy to contribute and more important than three points.
“I think it starts from the gaffer, he always wants us to get more and more.
“I think a lot of sides could settle when we scored two or three, but you can see the whole team, we wanted to push on and score more goals, and we did that."
City were leading at half-time but really came alive with four goals in the second half.
“I think we had a lot of control in the first half. They set up well they were frustrated with us at times.
“We kept the ball, but I don't think we had too many good openings. Obviously, Paris (Maghoma) is on fire, so we needed that.
“Then the second-half they opened up a little bit and we exploited it.
“It's just a change of game into the second-half. I felt we dealt with what came up.
“We knew, obviously, they're the home team, they're 1-0 down and, you know, they had to come out and press us.
“I felt like we'd done really well to find the spaces in behind. And yeah, look, we've done that.”
Darling believes the two-week international break won’t hinder their recent form.
“It's been a really hard couple of weeks, it's been a lot of games.
"Yes, we are on a winning run and when you're on this run you sort of want to keep going, but it's nice having a rest, but like I say, it'll be nice to play."