Third from bottom Sunderland have already conceded 26 goals in 13 league games this term and Allardyce left no doubts that defensive stability was his top priority.
"We have to stop the goals going in," he told a news conference ahead of Saturday's match with Stoke City.
"The defence was what kept Sunderland in the Premier League last year because the two leading scorers were Connor Wickham and Steven Fletcher with five each.
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"If we get 13 clean sheets this year we'll stay up. The most important thing is if we can continue to be very difficult to beat, to score against ... that is the starting point," said Allardyce.
Sunderland, who have nine points, kept their second clean sheet of the campaign when they beat Crystal Palace 1-0 on Monday and Allardyce was encouraged by their defensive display against Alan Pardew's team.
"The best thing for me was how few mistakes we made. We cut out those sort of errors we have been making on a regular basis that have cost us so many goals," he said.
"It is a big bonus for us, securing our first win away from home, and the way we achieved it shows the lads have got plenty of fight in their bellies.
"I think we are going to need a lot of fight and grit and determination to get out of the position we are in," Allardyce said.
Jermain Defoe will be available for the clash with 11th-placed Stoke despite limping off against Palace while fellow striker Fabio Borini is also available.
(Reporting by Simon Jennings; Editing by Tony Jimenez)
