The former Bolton manager made nine changes overall as a result of a large number of sidelined players, as well as the suspended Kevin Nolan. Forest took full advantage of a makeshift and inexperienced London side, with youngster Jamie Paterson grabbing his first hat-trick for the club.
West Ham sit one point above bottom-placed Sunderland in the Premier League, and Allardyce admits it has been a disastrous period for him and the club, primarily as a result of the number of absentees.
The Hammers’ boss told reporters: “It’s a disaster for me at the minute, a total disaster. I’ve got my hands tied behind my back every time I come in and see what’s available and what selection processes I’ve got, and the team is almost picking itself because it’s all I’ve got available at the moment.
“At the end of the day I’ve had to put too many youngsters in [the team] altogether, there’s no doubt about that, and they’ve not been up to the pressure and Forest have overrun us in the last quarter of the game.
“The lads playing on the field have got to realise it’s important not to open up and not let it be too easy to let the opposition go through and score the type if goals that they scored.
“It’s a great learning curve for them, but obviously nobody ever wants to get beaten 5-0."
Asked if the result would damage the club's youngsters mentally, Allardyce responded: “No, not really. I think what they have found out what level they’ve got to get to as young professionals, how dedicated they’ve got to be, how strong, not just in physical terms, but also in mental terms.
“This is not an easy game for so many to step into, but what it is, it’s a fantastic opportunity for them to realise [this], because they probably thought they were better than they were today.”
Forest boss Billy Davies, meanwhile, was understandably in a buoyant mood and was delighted with the win and happy to see his side carry their league form into a big cup tie.
“Our play has been very good [recently], there’s no doubt that we create a whole host of chances and there’s a great confidence in the side at the moment. I’m obviously delighted with the goals that we scored, I’m delighted with the clean sheet and delighted with the performance.”