The Sky Bet Championship side's emphatic 5-0 win - courtesy of Djamel Abdoun's cheeky 'Panenka' penalty, Jamie Paterson's second-half hat-trick and Andy Reid's late finish - might go down in some quarters as a cup upset but once the team-sheets were announced the bookmakers had already installed the hosts as favourites.
Allardyce, with injury and suspension problems and a Capital One Cup semi-final in midweek, handed out a total of five debuts, three from the start and two more off the bench, among nine changes to his team.
It was a gamble that backfired horribly as the relegation-battling Hammers simply had their confidence further assaulted by lower-league opposition.
The young rookies - Seb Lletget, Danny Whitehead, Callum Driver, Reece Burke and Blair Turgott - can hardly be blamed for the humbling result, but Allardyce may not be as lucky.
His future may detract slightly from Paterson's efforts, but it should not - with the winger winning his side's spot-kick and then converting three fine goals of his own.
The opener came after just 12 minutes as Paterson beat George Moncur with some neat footwork before being tripped by the midfielder.
Martin Atkinson pointed to the spot but when Abdoun reached for the ball, Forest fans appeared to groan in unison.
They need not have worried, though, as the Algerian dinked the ball down the middle with a supreme confidence not usually associated with a player who had never previously scored for the club.
West Ham's most experienced players were stationed on either wing, with captain-for-the-day Stewart Downing left and Matt Jarvis right.
Their response to the goal was to look for the pair with every attack and in the 23rd minute, the Hammers went close to levelling.
Reid's foul gave Ravel Morrison a chance to test his free-kick skills from 20 yards out and his bending shot would have crept under the crossbar had Karl Darlow not responded with a fine save.
Having survived that, Forest went again - Gonzalo Jara splitting the away defence with a slide-rule pass that former Hammers loanee Henri Lansbury just failed to reach.
There was a big penalty appeal soon after when Driver went in hard on Greg Halford as he looked to convert from close range, but the defender did seem to get a piece of the ball.
Regardless, West Ham were clinging on - goalkeeper Adrian tested first by Jamaal Lascelles' long-ranger and then by Halford's downward header.
A rare counter-attack in the 35th minute almost yielded results but just as Modibo Maiga set himself to shoot, Eric Lichaj made a wonderful blocking tackle.
Three minutes before the break, Forest missed two more chances to double the lead.
Reid's clever through-ball deserved a better finish than Eric Lichaj could provide and, when Adrian's save came back out, Lansbury shot over from an inviting position.
Forest started the second half at a fierce pace but Abdoun, emboldened by his goal, repeatedly made the wrong decision - shooting when he should have passed and almost costing his team dear with a 40-yard cross-field pass directly to Downing.
Allardyce's side could not take advantage of that sloppiness, Downing's shot deflected over and Whitehead following up with a wild attempt of his own.
The manager responded by throwing on more youth, handing two more debuts to Burke and Turgott and also sending on the callow Mathias Fanimo.
The Premier League side might have equalised before the hour mark had it not been for Darlow, who saved low from Lletget while unsighted and stood firm to Morrison's near-post drive.
That was as good as it got, though, with the game ended as a contest on 65 minutes when Halford held the ball up well before teeing up Paterson.
He opened his body and found the bottom corner, despite Adrian's best efforts, to put the result to bed.
Paterson's second came just six minutes later as West Ham's frailties continued to be exposed. Lansbury played creator this time, squaring the ball for Paterson, who stroked home confidently with a first-time effort.
By now, Forest were all over their opponents - Lansbury, Paterson and Abdoun taking turns to torture their young markers.
Paterson's hat-trick now appeared to be their priority and the Hammers did not look up to the task of denying it.
With 11 minutes to go he raced into the area, shuffled into a shooting position as defenders stood off and deposited neatly into the bottom corner.
There was one final insult when Reid smashed home Abdoun's lay-off in injury time, leaving West Ham thoroughly humbled and with plenty to ponder.