The Baggies take on Leicester on Thursday, and then face Villa on Sunday, knowing they are going to need a significant points haul to keep alive their hopes of staying in the Premier League.
But while they currently sit nine points from safety, they head to the King Power Stadium full confidence following two outstanding displays against Chelsea and Southampton.
Allardyce's men thrashed Chelsea 5-2 at the beginning of the month before following that win up with a comprehensive 3-0 victory over Southampton.
And the boss has now demanded his players maintain those standards until the end of the season.
"We have changed our fortunes in a very positive way," the former Crystal Palace manager said.
"It’s not just me, it’s all the coaches and the backroom staff that are here – they are all working tirelessly to try and change our fortunes.
"I have never seen a team who has been struggling against relegation destroy a team like Chelsea the way we did.
"We came close to it at Crystal Palace when I was there – we beat Arsenal 3-0. But it wasn’t as good as that one against Chelsea.
"We then put in another top-quality performance against Southampton.
"Now I am in the position of saying to the players they really need to not lower the standards they have shown.
"I’m demanding from them that they stay at that level until the end of the season – because that level will be needed if we are to maintain our Premier League status."
Meanwhile, Monaco are the latest club being linked with a move for Albion loanee Ainsley Maitland-Niles.
The England international has impressed in nine outings for the Baggies since joining on a temporary basis from Arsenal.
Keen for regular first-team football, Maitland-Niles could leave the Gunners permanently this summer.
And according to reports, Monaco have joined Crystal Palace, Wolves, Leeds and Leicester in the race to land the 23-year-old.