West Brom dismissed head coach Irvine after less than seven months in charge on Monday following a disappointing first half of the Premier League season.
They won just four of their first 19 games of the campaign, and sit only one point clear of the relegation zone after three straight defeats - the latest of which came at Stoke City on Sunday.
It remains to be seen who West Brom will turn to to replace Irvine permanently but, ahead of their trip to Upton Park on New Year's Day, West Ham boss Allardyce is wary of an immediate response from their players.
"I think initially it [facing a team after a sacking] can be a disadvantage," Allardyce said. "When West Brom experienced change [with the appointment of Pepe Mel] last year we played them soon after and we lost 1-0.
"For us it's about trying to re-establish our winning ways because we had a run of seven unbeaten at home [prior to Sunday's 2-1 loss to Arsenal].
"West Brom will be a tough game, I saw their game against Manchester City [a 3-1 loss on Boxing Day] and they created a lot of chances. They'll be a threat and we need to be aware of that. It was a tough 2-1 win for us earlier in the year."
Festive defeats to London rivals Chelsea and Arsenal have dropped West Ham out of the top four, cooling talk that they could potentially push for a UEFA Champions League place.
Allardyce has a near fully fit squad to choose from as West Ham bid to get back to the form that has surprised many this term, with defender James Tomkins their only absentee due to suspension.
James Collins is poised to come in for Tomkins, while on-loan Arsenal full-back Carl Jenkinson is available again after being ineligible to play versus his parent club.
By contrast, West Brom caretaker boss Rob Kelly has a number of injury problems to contend with.
Midfielder James Morrison (knee) and winger Stephane Sessegnon (calf) both picked up knocks in the 2-0 defeat to Stoke.
That pair join Sebastien Pocognoli (knock), Victor Anichebe (groin), and Georgios Samaras (lack of match fitness) as doubts, while Jonas Olsson is out with an Achilles issue.
Kelly is aware of the threat posed by West Ham, but is confident West Brom have the players to cause Allardyce's men plenty of problems.
"They've [West Ham] moved forward, they've moved it on again. I'm not overly surprised [with their form]," Kelly said.
"They ask questions of you in your last third. They're very good with balls into your box, with set plays, they've got some good individual players but so have we.
"We're aware of their threats but we've got threats of our own."
