Allardyce, however, expects a tough encounter against Everton, who have came under heavy criticism for their timid display in Saturday's 3-1 loss to champions Leicester City.
"We've got two games left to secure Premier League status but knowing we can kill everyone else off on Wednesday is pressure in itself. Can we handle it?" the 61-year-old Allardyce told British media.
"Everton will be out to spoil our celebrations. Roberto's players will fight all the way because of the criticism they received after their defeat at Leicester at the weekend."
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With Sunderland flirting with relegation for the last four seasons, Allardyce hoped his serial strugglers will learn from their mistakes and avoid another relegation scramble next campaign should they stay up.
"Let's do it for the fourth time and say, let's not let it happen again. I think that's the most important thing," said Allardyce, who has never been relegated from England's top-flight as a manager.
Failure to beat 12th-placed Everton could ensure a nervous final day for Sunderland, who finish their campaign with a trip to Watford at Vicarage Road on Sunday.
(Reporting by Nivedita Shankar in Bengaluru; editing by Sudipto Ganguly)
