Newcastle were able to bounce back after their defeat at Sunderland.
Asked how tough the week had been, Gouffran said: "It was really, really difficult. It was an exhausting match for us against Manchester City. We lost in extra-time, so we had to play that much longer.
"Coming off the back of a derby defeat, we were very disappointed. We know we could have done a lot better in the week.
"It was disappointing to have lost it and we had to go out there and show a really different side of ourselves on the pitch and really make it up to the fans, and we did that."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball