Gus Poyet's side have gone six games without a win in the league and sit bottom of the table with 10 points from 17 matches.
|25/1||Sunderland are 25/1 with BetVictor to beat Everton 1-0|
"You need to keep believing because that's what takes you out," he told the Shields Gazzette.
"We beat Man City, Newcastle and Chelsea, so I don't see why we should give up the fight.
"We'll keep putting the full effort in. We might not win against Norwich, but we might win against Everton. You never know.
"Every game is a final. It was before, but even more so now.
"You have to realise that it's our life. If I'm going down, then I'm going down and my team-mate is too.
"We need to be better than to come out of this situation because otherwise we're all going down - us, the fans, the club, everybody."
Sunderland will spend Christmas Day at the foot of the table, and only once in the Premier League era has the side who is bottom on December 25 avoided relegation.