Gouffran struck in the 1-1 draw at West Bromwich Albion on Saturday.
Gouffran said: "Sunderland have started picking up points but it would be great to finish above them at the end of the season.
"It would be sweet for the fans. We know the derby was a very important game, so we were disappointed because we really wanted to play well in it.
"It was embarrassing. It was a good time to not be able to speak English! Even though I'm not from Newcastle I still understood the importance of the game.
"We spoke a lot after the derby because there were things we wanted to improve on. We really wanted to follow that defeat with a good performance here. We had to show we are a strong team and to forget last week's result.
"You saw in the first half, the improvements we made, we just weren't able to sustain it. But as a group of players, we are confident we can escape relegation."