Gopperth and company will end 2011 propping up the league table whatever happens against Northampton at Kingston Park on Saturday.
Newcastle are six points adrift of 11th-placed Worcester and a further two behind Bath in 10th, with the Premiership season at its halfway point.
Saints will arrive on Tyneside as the competition's form team having amassed 22 points from their last six games, although the Falcons have not been grounded at home since Leicester beat them more than three months ago.
"We can't worry about what is going on around us. We must concentrate on ourselves," said fly-half Gopperth, who has scored two thirds of Newcastle's Premiership points this term.
"We have to believe that we can pull off the wins, and we have certainly got the team to do it. Hopefully, we can stay injury-free.
"The main thing is to keep believing and those wins will come."
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