And Allardyce knows his side must maintain that standard ahead of another must-win match against Leicester on Thursday.
"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 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."