Sunderland picked up their first win of the season by beating their near neighbours, and they moved off the bottom of the Premier League table as a result.
However, Allardyce was not entirely satisfied with the performance, and he still sees areas where his side will need to improve, if they are to get out of trouble.
“We’ve got a lot of work to do,” he said. “We’ve got to be a lot better than we were today.
“Enjoy the victory, yes lads, and well done, but we have to be a lot better than the performance we put in today if we are to get out of trouble and get into midtable.
“I’m going to be pushing the lads to get better than this performance. That might sound a bit harsh, but for me I think we need to get a bit better.”
Sunderland were second best for much of the first-half of the fixture, but the game turned on a controversial red-card for Newcastle defender Fabricio Coloccini.
The Argentine centre-back was deemed to have denied a clear goalscoring opportunity, when he barged Steven Fletcher in the penalty box and was banished from the field.
Sunderland went on to score the resulting spot-kick, and their numerical advantage ultimately was decisive, as they went on to record a comfortable victory.
The Black Cats scored goals through Adam Johnson, Billy Jones and Fletcher, as they recorded their sixth victory in a row over their fiercest rivals and took a big step closer to safety.