With four matches to play - the first a daunting trip to title-chasing Liverpool on Sunday - Newcastle are in the drop zone in 18th place, three points behind Hull City who occupy the relative safety of 17th place.
"We can't get our heads down. There's still a lot of work to be done and we're still in there fighting," Shearer, appointed as manager for the final eight games of the season, but without a win after four games in charge, told Newcastle's television channel nufcTV on Wednesday.
"There'll certainly be no despondency and no-one will be giving up the fight. We will go to Anfield in good spirits and see what we get. Obviously we go there as underdogs but we must believe we can get something."
Shearer has pinned much of his own faith on striker Michael Owen re-discovering his scoring touch after nine games without a goal and Owen said his goals can still keep Newcastle up.
Following Newcastle's 0-0 draw with Portsmouth on Monday Owen, who will be desperate to end his barren streak against his old club at Anfield, said: "I wake up and know where I stand in terms of performances, my standing in the game, the goals I will score given the opportunities and everything else.
"I have been around a long time and everyone knows if I get chances I will score goals. We understand the criticism we've received for where we are in the table, but we also know for a fact we are a better team than we are showing on a regular basis.
"We have to be brave and positive. We go to Liverpool and we finish the season at Aston Villa, and if we can get some points from those games we'll grasp them.
"But it's the next home games against Middlesbrough and Fulham that are the major focus."
Newcastle have won only one of their last 18 matches in all competitions and unless their form improves dramatically in the last few games they will be in the second tier of English soccer next season for the first time since 1993.
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