Everton have not won a league game for over a month and could be without the services of defender Seamus Coleman, who has picked up a stomach bug.
"Our job on Sunday is to make Roberto (Martinez) as miserable as we did last season," Allardyce, whose side are third from bottom in the table, told reporters at his pre-match news conference.
"We can't overshadow that we have to play better and we have to do more. If we can't win we have to make sure we don't lose."
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"We have to produce week by week and game by game. We have to dig in and get results."
The manager acknowledged that he had a fight on his hands to stave off relegation, but expected his team to take confidence from the win over Newcastle.
"We have to meet it head on but we have to enjoy ourselves. It can't be all doom and gloom -- it's our job to lift the players," he said.
"We were delighted to win the derby but we hope it gives us the confidence to go on from here. The hard work starts now."
The former West Ham United manager is sweating on the fitness of injured quartet John O'Shea, Younes Kaboul, Ola Toivonen and Fabio Borini, and will have to wait until the last minute to see if any of them can play.
"We may have to juggle around the team and the system due to injuries and the way Everton play," Allardyce said.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
