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."
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."
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