The Baggies have put in vastly improved displays against Manchester United and Burnley in recent weeks – despite being held to a draw both times.
Allardyce’s men had some excellent chances to beat Ole Gunnar Solskjær’s side.
While they also dominated Burnley and again should have won despite playing for over an hour with 10 men.
Key to those performances have been new recruits Robert Snodgrass, Ainsley Maitland-Niles, Mbaye Diagne and Okay Yokuslu.
Allardyce has been delighted with all four player since they arrived at The Hawthorns. And he feels Yokuslu and Diagne particularly deserve praise for how they have adapted to the Premier League after arriving from Celta Vigo and Galatasaray respectively.
“The new faces have been magnificent,” Allardyce said.
“It’s not as difficult for Robert Snodgrass or Ainsley coming in from Arsenal.
“But it’s certainly difficult for Okay and Mbaye to perform the way they’ve performed right away in the Premier League.
“They’re two players who have hit the ground running and have instantly made us better as a team, as well as Ainsley and Robert, and that’s affecting all the other players around them.
“They’re starting to play better because the confidence is growing.
“The sad thing is that the confidence should be sky high because we should have beaten Burnley and Manchester United. But unfortunately we didn’t.”
Meanwhile, defender Kyle Bartley admitted he too has been impressed with Yokuslu since the holding midfielder arrived from Spain.
“He’s been brilliant,” the defender said.
“He seems to have settled in really quickly which is always important for a player at a new club.
“You can see already that he’s a really good player.
“I thought he was great against Manchester United on his full debut and then he backed that up with another impressive performance on Saturday against Burnley.
“He’s tenacious. He’s good on the ball. He’s calm and composed.
“I think he’s made a big difference in there.
“I hope he can continue the form he has shown in the last two games from now until the end of the season.”