The Hammers were booed off in their last match - despite beating Hull City - while Gus Poyet's men are four points from safety with nine games of their season left to play
Allardyce endured the wrath of the Upton Park boo boys following Wednesday's Premier League clash with Hull City, despite guiding his men to a 2-1 victory.
A Mark Noble penalty and a James Chester own goal ensured that the east London club secured all three points after Hull goalkeeper Allan McGregor was sent off in the 24th minute but the performance was jeered by a section of the club's supporters.
Allardyce is confident , however, that he has the backing of the majority of fans ahead of Monday's trip to the Stadium of Light.
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"In the cold light of day, everyone realised how important that win was and everybody has got to realise what we have done in the last eight games - we've got 15 points in those eight games and that is about a top-six finish in the Premier League, or at least a top-eight [finish].
"The frustration was understandable because when people see you are playing against 10 men, they think it's easier. We know, as professionals, that it's not that easy and that proved to be the case.
"The most important thing was to win the game, acquire the three points and try to push on from here."
For Sunderland, who won this fixture 3-0 last season, the sole focus will be on picking up the three points once again. Gus Poyet's charges still languish in the bottom three but will have games in hand on every other team in the top flight at kick-off.
Having failed to win any of their last six matches in all competitions, midfielder Ki Sung-Yueng - on loan from Swansea City - is under no illusions as to the importance of Monday's fixture.
"We're all aware of what we need to do in the next game - it's crucial," he told the Black Cats' official website. "If we get three points from that one it could see us move up the table and close the gap.
"We're the home team and West Ham are coming to play us; we need to match them and take the game to them to make sure we take something from it."
Sunderland will be without striker Steven Fletcher (ankle) again, while Keiren Westwood remains on the sidelines with a shoulder injury, but on-loan forward Fabio Borini is back in contention after missing the 2-1 defeat to parent club Liverpool in midweek.
James Collins (calf) is definitely out for West Ham but fellow centre-back James Tomkins could be involved despite a knock.