The Black Cats have a tough set of matches on the horizon, with their next five games coming against some in-form sides in Southampton, Crystal Palace, Stoke, Arsenal and Watford.
And Allardyce says that he is aiming to for his team to be on more than 10 points by the time they make it through that run of fixtures.
“We broke down the first eight games,” Allardyce said in the Sunderland Echo.
“From our point of view, we’ve played three games and got three points, and got five games to go.
“At the end of that five games, we have to have better than double figures. That’s what I’m looking for.”
Allardyce’s point target is relatively modest, considering Sunderland are already playing catch-up due to their poor start.
The Black Cats have won just once this season, against Newcastle United, and they are currently sat down in 19th place in the Premier League table.
Allardyce’s men are two points away from safety, and their latest performance was a very disappointing one.
Sunderland showed attacking promise against Everton, but they went down 6-2 at Goodison Park, and they will have to tighten up defensively if they are to match Allardyce’s target in the coming weeks.