Goals from Steven Gerrard, who rammed the taunts of the home fans back down their throats following England's midweek disaster with a fearsome 28th-minute free-kick, Dirk Kuyt and substitute Ryan Babel were more than enough as the Magpies tamely surrendered.
Owner Mike Ashley is unlikely to react to the boos which rang around St James' Park at both half-time and the final whistle but Allardyce knows he faces an uphill task.
He said: "I have never quite found myself in this predicament before to be honest with you.
"But I have dealt with some difficult situations and this one is a good challenge.
"You roll your sleeves up and you get on with your job. You know what's right and you know what's wrong and you get it put right.
"Hopefully, that starts at Blackburn Rovers next week."
Allardyce took the opportunity this week to rule himself out of the race to replace Steve McClaren as England manager.
However, the home fans sang, ironically, "Big Sam for England" and "You don't know what you are doing" as Allardyce bewildered them with his substitutions to take a tense relationship to the point of breaking.
"We have hit rock-bottom at the minute and we have got to get ourselves out of it," said Allardyce.
"There's only us who can do it by sticking together and trying to get as many players fit as we possibly can and showing a lot more grit and determination to acquire that result."