The Black Cats have failed to win any of their opening eight Premier League matches, throwing away a 2-0 lead in their most recent fixture against West Ham United - a game which proved to be Dick Advocaat's last in the managerial hot-seat.
And their poor run of results has left Allardyce concerned, as he believes that the team's morale could be in a fragile place at the moment.
“It is about stopping the goals we have been conceding," he said. "If we can do that it will rebuild the confidence of the team and the players’ confidence is my biggest worry. Are they still confident enough to go out and perform at this level and overcome the doubts they have in their minds? I need to get them out there and get them believing.”
Allardyce's first game in charge of the Black Cats comes against West Bromwich Albion this weekend at the Hawthorns.
It promises to be a testing bow for the experienced boss, but Sunderland may feel that they have a chance of getting something from the game, if they can raise their performance levels.
West Brom have been difficult to beat this season, but they have found goals hard to come by, and have only hit the back of the net six times.
Sunderland have gifted the opposition goals on numerous occasions so far this term, but if Allardyce can spark an improvement in their defensive cohesion, they will stand a chance of returning with the points on Saturday.