"We are some distance from safety (five points) and while some people say that is only two wins, actually winning two on the trot is a big ask.
"It could take up to six games to catch those teams up but there are 21 games to go, we've got a relatively fit squad and it's about lifting their confidence and using the old adage of taking it one game at a time."
Allardyce is hoping that he brings the same immediate success to Ewood Park as Harry Redknapp did at Tottenham following his switch from Portsmouth.
"I hope I have a Harry Redknapp Midas touch when it comes to Saturday," Allardyce continued.
"Things have become very rosy almost instantly for him and I hope that works for me in a difficult game against Stoke on Saturday."
Allardyce has wasted little time in stamping his mark on the club by appointing Neil McDonald as his assistant manager.
McDonald worked with Allardyce at Bolton and his arrival means two of Ince's backroom team, Ray Mathias and Archie Knox, have followed the ex-Manchester United, Inter Milan, Liverpool and England midfielder out the door.
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