The Black Cats take on West Ham United this weekend after a big win over Manchester United boosted their confidence.
The Black Cats beat Louis van Gaal’s struggling side 12 days ago, with that victory providing a huge boost to their hopes of escaping relegation this season.
This weekend sees Allardyce’s side face another tough game as they travel to Upton Park to take on his former side West Ham United.
And he says he is hopeful they can continue where they left off last time around, saying he has sensed a change in the players’ mindsets after that big win.
“One would like to think we can continue where we left off against Manchester United,” he told safc.com.
“I sense the players have got more belief in themselves, with the recent results and I sense they feel more comfortable with the situation to try and strive to get away from the bottom three.”
“We have to try and maximise our points total as much as we can to alleviate our position.”
Allardyce will now be hoping that the win over United can be the springboard to his team avoiding relegation this season.
They are currently 19th in the table on 23 points, just a point behind rivals Newcastle United and Norwich City in 18th and 17th place respectively.
That means they are very much in with a shout of pulling clear, with the likes of Swansea City and Bournemouth above them not out of danger yet either.
And Allardyce will be keen to see if Sunderland's new found belief can see them beat his old team this weekend and continue that climb away from danger.