Allardyce is famed for his ability to get sides organised, but the Black Cats have looked porous at the back, even under his stewardship.
Sunderland have conceded 53 goals in their 28 Premier League matches to date, giving them the joint-worst defensive record in England’s top flight.
And Allardyce believes that Sunderland will continue to struggle, unless they can start shutting opposition sides out.
“Still the ultimate problem is the ultimate problem – we concede too many," he said.
“Until the lads get a grip on themselves and say, ‘We’re going to score one goal and win this game with that’, then it’ll stay like that.
“We haven’t won a game 1-0 since I’ve been here. When the pressure comes on, that’s what you have to be capable of.”
Sunderland’s defensive issues were highlighted in their last match against Crystal Palace.
The Black Cats had taken the lead against Alan Pardew’s side in the first half, when Dame N’Doye scored from range.
However, Palace hit back in the second half, with Connor Wickham scoring twice to turn the game on its head.
Sunderland then had to rely on Fabio Borini’s last minute wonderstrike to rescue a point.
That draw did move Sunderland above the relegation zone, but their position in the Premier League is still far from secure.
The Black Cats’ next match comes against Southampton on Saturday.