Premier League Preview: West Ham v Sunderland
Sunderland were 4-0 down by half-time at home to Aston Villa last weekend and, although Tim Sherwood's side did not add to their advantage after the break, the poor display was enough to cost Gus Poyet his job.
Poyet's exit paved the way for the experienced Advocaat to arrive on Wearside on a short-term contract, with Sunderland a point clear of the relegation zone.
"They've moved swiftly to make a change and give themselves the best possible chance of getting the points they need," said Allardyce.
"The players at Sunderland will be hurt that they've let the fans down with a 4-0 defeat last week and I think we'll have a very tough game on Saturday."
Allardyce, along with Advocaat, is among the favourites to take the Sunderland job on a permanent basis come the end of the season.
However, his main focus for now is on securing as strong a finish as possible with West Ham - 10th in the top flight having fallen away in recent weeks - who will be without Andy Carroll (knee), Enner Valencia (foot) and James Tomkins (shoulder), while Winston Reid (hamstring) faces a late fitness test.
"It's an opportunity for us to start a comeback this weekend," Allardyce continued. "We can't feel sorry for ourselves as every team has injuries at some time in the season and it's about overcoming that,
"We've had a challenging run of fixtures and we should have taken more points than we did, which would have put us in a fantastic position.
"No Andy Carroll, no Enner Valencia at this time means we haven't got the strength in depth that we're looking for. With Winston Reid and James Tomkins too, that's the spine of our team and it's a big ask on the players.
"But, that said, I expect them to give a big performance and this game is as big for us as it is for Sunderland."
Sunderland - who have Lee Cattermole suspended - could be without Steven Fletcher (thigh) after the striker was forced off during the defeat to Villa, while it is unclear whether Adam Johnson will be involved after his suspension was lifted on Wednesday following his arrest and subsequent bailing.
Midfielder Jack Rodwell said: "It is a massive game and we were obviously hurt following the last game against Aston Villa, so we have to make that motivate us because this game is crucial and we need three points to bounce back."
The teams drew 1-1 at Sunderland earlier this season - Stewart Downing cancelling out Jordi Gomez's 22nd-minute penalty.