"We will go into the big games as the underdogs and tell the lads to enjoy themselves because nobody expects you to get a result," Allardyce told the club's website (www.safc.com).
"Hopefully we can shock one or two because the lads have enough confidence in their ability to play any team at any time.
"You can beat them if you're on song and you take full advantage of what you create, so let's hope that is the case."
The Black Cats, who are fourth-from-bottom in the table and two points above the relegation zone, are likely to be without striker Jermain Defoe and midfielder Sebastian Larsson for Saturday's trip to the Emirates Stadium to take on Arsenal.
"Jermain suffered an injury to his hamstring and obviously Seb Larsson medial ligaments," Allardyce said.
"Hopefully they will be fit as quickly as possible – they probably aren't going to be fit for next weekend but hopefully the week after."
(Reporting by Shravanth Vijayakumar in Bengaluru. Editing by Patrick Johnston)
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