The result leaves Sunderland second bottom the of Premier League on 12 points, six points adrift of safety and with the worst goal difference in the top flight.
Sunderland entertain Jurgen Klopp's Liverpool side tomorrow knowing they must start finding wins, particularly at home.
As the record goalscorer in Premier League history, Shearer's views carry a lot of weight even if it is hard to hear from their bitter rivals' best ever player.
The BBC pundit, who scored 313 goals in 622 career games for club and country, told Match of the Day Sunderland look doomed, unless Allardyce can tighten up his defence with some signings in January.
"They're a soft touch," Shearer said on MOTD.
"Thirty-seven goals they've conceded already this season and 16 in their last five away games.
"If Sam doesn't go out and buy some defenders in the January window then they're as good as down I think."
Will Sunderland risk panic buys?
Making panic buys in the typically extortionate January market always comes with a huge risk when the team could find themselves in the Championship five months later.
But with the money due to come into the Premier League through the latest bumper TV deal next season, clubs in danger may have to speculate to accumulate.
If Sunderland do drop it will end Allardyce's proud record of having never been relegated from the Premier League.
Many pundits and supporters felt the appointment of the former West Ham boss would all but guarantee the Mackems safety.
But with just three wins and seven defeats from this first 10 games in charge that record looks in jeopardy and Shearer's prediction is difficult to contest.