The Magpies legend believes it could be "curtains" for the club if they lost at Norwich City in a fortnight's time.
The Magpies salvaged a draw against arch-rivals Sunderland in Rafael Benitez's first home match in charge of the club thanks to Aleksandar Mitrovic's late header, which ended a run of four straight defeats.
However, despite their poor record against the Black Cats in recent years, a home clash against another club battling to survive undoubtedly represented one of the best chances for Benitez's men to get vital three points on the board in the closing stages of the season.
The Magpies now face 17th-place Norwich City after the international break before facing tough challenges in Southampton, Manchester City, and Liverpool in three of the next four matches following the clash with the Canaries.
Desperately worried for his former side's survival, Shearer is concerned that defeat at Carrow Road, which would put six points between the North East club and the East Anglia side, would spell the end for Benitez's men.
He told BBC Sport: "After being 1-0 down with seven minutes to go, it is a positive that Benitez has got his first point on the board, but he has got another gigantic game coming up when his side play Norwich after the international break.
"The Canaries will go into it full of confidence after two clean sheets on the spin and four points from their past two games against West Brom and Manchester City.
"Losing to Sunderland would have been bad enough as it would have left Newcastle four points adrift of safety - but the Magpies simply cannot afford to be beaten at Carrow Road. If they do lose, it is probably curtains for their survival hopes. The Canaries would be six points above them."
Newcastle do have other fixtures against uninspiring teams yet this season, facing Swansea City on 16 April and a desperately short of form Crystal Palace side in their penultimate home match.
Their fate is also likely to be affected hugely by the result of the clash between Sunderland and Norwich on the same day as the Magpies host the Swans, with any two of those three clubs almost certain to join Aston Villa in the Championship.