Sunderland, who are seven points adrift of safety, head into Wednesday's game against Liverpool with 12 defeats in the league this season. Only fellow relegation strugglers Aston Villa have more, with 13 losses.
"We have just got to stop losing," Allardyce told British media. "If we draw two, then that is no problem. If we can win one, that would obviously be much better. If we could win two, fabulous.
"Our problems at the moment are very acute defensively, which is making life extremely difficult for us, but we have to also show a lot more grit and determination than we are showing at the moment."
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Sunderland begun well under Allardyce after the Englishman replaced Dick Advocaat at the Stadium of Light in October, winning three of his first six games and moving team temporarily to 17th place, out of the relegation spots.
However, over the past few weeks they have been brushed aside by Arsenal and Chelsea, while Manchester City romped to 4-1 win on Saturday.
"We have just not applied ourselves out of possession defensively correctly -- certainly in the last two games," the manager added. "They are big teams, but they are big teams who have not been playing that well.
"City barely beat Swansea, and Chelsea had sacked (manager) Jose (Mourinho) and were low on confidence, but we made life extremely easy for both of those teams and that really worries me about our defensive resilience.
"We need to be more active out of possession in closing down the opposition better."
Following Liverpool, Sunderland host Aston Villa on Saturday, before visiting Arsenal in the FA Cup a week later.
(Reporting by Nayan Das in Bengaluru, editing by Pritha Sarkar)
