Worcester are just one spot above the 12th-placed Falcons, but the gap between them grew to nine points after Warriors beat Leicester last weekend.
Defeat at Kingston Park for Newcastle would leave them with a mountain to climb, but Richards has no intention of throwing in the towel.
“When you look at the fixtures we’ve got between now and the end of the season, there is no reason why we shouldn’t stay up,” rugby director Richards said.
“We just need to start winning, and Sunday should be the start of it.
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“A key part of our approach to this game is to keep a lid on all the stuff going on around it and just focus on the processes needed to put in a good performance.
“The side which can maintain its focus and control is the one that will win the game, in all probability, because overall we are two fairly evenly-matched teams.”
Scotland international flanker Gary Graham returns for Newcastle, while prop Logovi’i Mulipola is also back, but injuries sideline a number of players, including Vereniki Goneva, Alex Tait, Joel Hodgson, Michael Young and Jon Welsh.
Wales wing Josh Adams is rested by Worcester, with an in-form Tom Howe again deputising, while full-back Chris Pennell equals Warriors’ Premiership appearance record when he features for the 149th time.
Newcastle have lost five successive Premiership games, including away to leaders Exeter last time out, with their last league success being against Northampton on December 1.
Richards added: “The guys fronted up physically last weekend, and we are lacking nothing on that side of things. We scored three tries against a good Exeter side, and we should have had a couple more.
“We had the opportunities, but left them out there on the pitch, despite putting together some good passages. But Exeter are top of the league for a reason.
“They (Worcester) have got dangerous wingers, an excellent scrum-half and some good props, just to pick out a few positions, and in many ways they’ve got strengths in similar areas to ourselves.
“It will come down to who can control themselves better on the day and who can execute their game-plan.
“On their day, any side can beat any other, and it wasn’t any surprise to us that Worcester were able to take the points late on against Leicester.
“Worcester are a side that we need to beat because of where we are in the league in relation to each other, and if we do then it opens it all up again.
“If we lose it becomes more difficult, but there are still seven games left after this weekend, and Worcester and (ninth-placed) Bristol have to play each other.”
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