The Blacks Cats have to take on the likes of Chelsea, Manchester City and Arsenal over the Christmas period.
The Black Cats won back-to-back games for the first time this weekend, with a 2-0 win over Stoke following up their 1-0 victory over Crystal Palace.
That win moved them out of the relegation zone, with Allardyce's men now sitting two points clear having pushed Newcastle into the bottom three.
They face a difficult set of fixtures over the Christmas period though, facing Arsenal, Chelsea and Manchester City on the road, as well as a tough home tie with Watford.
And Allardyce has urged his players to cause a few upsets against the bigger sides.
“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,” he told 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.”
While moving out of the relegation zone was a big boost for Allardyce’s side, they will know that the job is far from being done yet.
They are just two points clear of Bournemouth and Newcastle in the relegation zone, meaning results going against them could see them back in the bottom three rapidly.
They will though, be boosted by the fact the clubs above them are not too far away with Chelsea in 14th place only three points above them.