Sunderland and Aston Villa are both looking to put together a run of three wins.
Allardyce realises that only a strong run of form will see his side move away from trouble, and he has set his team the challenge of picking up three wins in the coming weeks.
“We’re going to have to win three out of four or something like that,” he said.
“We’ve got to that stage now and it’s all about how early we can do it.
“Some teams will do it, and we’re going to have to be one of them."
Allardyce’s win target is exactly the same as the one which Remi Garde has set for his Aston Villa side.
Villa are currently the only side below Sunderland in the top flight table, and they are 10 points away from safety.
And Garde believes that only a run of three consecutive victories would give his side any chance of escaping relegation.
"I still believe we can win two or three games in a row - then we will be back on track," the French boss told Villa's official site.
"I will be lifting my players. They give me a lot of hope in the previous weeks and the previous games."
Sunderland’s next match comes against Liverpool at Anfield tomorrow, while Garde’s side are set to take on Norwich City in a must-win match at Villa Park.