Allardyce made nine changes for the third-round tie at the City Ground, handing debuts to three rookies in his starting XI and two more from the bench.
His youthful side were comprehensively and deservedly thrashed by Forest, for who Jamie Paterson scored a superb second-half hat-trick in between Djamel Abdoun's penalty and Andy Reid's injury-time effort.
With his side second bottom of the Barclays Premier League and boasting just one win in their last nine matches, Allardyce knows time is running short to turn things around, but defended his cup selection.
Allardyce has the first leg of the Capital One Cup semi-final against Manchester City to come on Wednesday, with key league games against Cardiff and Newcastle before the return fixture.
With that in mind he informed co-owners David Gold and David Sullivan he would have to make major alterations for Forest ahead of time.
Asked if he expected repercussions, he said: "There might be, who knows? It's their decision, not mine.
"I'm not saying it won't happen unless I start to get results. I have got to get results, I know that.
"But I made them (Gold and Sullivan) aware of what would happen today because I'm not in the position to go and do these things without telling everybody internally what is planned for the next few games."
Allardyce made no apologies for his decision to place the trip to Nottingham down the pecking order, with the relegation battle the most pressing ambition and a possible - if unlikely - trip to Wembley next down the list.
"My priorities meant I put too many youngsters in and they were not able to withstand Forest's pressure in the last half an hour," he said.
"I picked the team so it is my responsibility. You know what my priorities are: the priorities are the Premier League first and then Capital One Cup.
"It's leg one on Wednesday and we need to get back to the second leg with an opportunity to get to Wembley and then get some points at Cardiff.
"My hands are tied behind my back every time I see what's available and the team is almost picking itself. It's a disaster at the moment, a total disaster and in certain areas we've not been able to cope."
The Hammers' most pressing concerns at present are in defence, where there are several injuries and - on this evidence - few ready to take up the mantle.
The January transfer window may help with that and Allardyce confirmed he was interested in, though not confident, of a move for Manchester City's Joleon Lescott.
"I don't know if Joleon is available, but if it is possible I would like to get him," he confirmed.