West Brom currently sit 19th in the Premier League table with 24 points and are nine points away from safety.
The Baggies have enjoyed back-to-back victories against Chelsea and Southampton in their last two league games and are looking to build on their good form in order to maintain their top flight status.
Allardyce, who has a track record of dragging clubs out of relegation scraps, has placed an emphasis on the importance of staying clear of any slip-ups in their remaining games of the season.
The former Everton manager stressed the Baggies’ good form must continue in order for them to lift themselves out of the drop zone.
Allardyce went on to reveal that his players are in a good place mentally as they head into the final seven games of their campaign.
“You can see that the lads are enjoying their football more and more”, Allardyce told West Brom’s official site.
“They are enjoying their football more because we have started to win games and play well at the same time.
“The players have to take a lot of credit for how they’ve performed in the last two games.
“We are in a good place at the moment and I hope we’ll all still be smiling after playing Leicester on Thursday night.
“We’re short on time and we’re short on games.
“There’s no margin for error really.
“We have to continue our good form.”
Allardyce will look to inspire his West Brom side to seize maximum points in their remaining fixtures as they mount a late challenge to stay in the Premier League.