The Hammers travel to the City Ground on Sunday languishing in 19th place in the Barclays Premier League and having collected just two points throughout the whole of December.
A 3-0 home win over Fulham on November 30 was the last time West Ham managed to take three points from a league game, although they have progressed to the final four of the Capital One Cup with a two-legged semi-final against Manchester City to come.
Those two factors dictate that Allardyce will not be focusing too much on their FA Cup tie at Forest but he feels they will not be the only club taking the competition a little lightly.
"There is no change from my point of view in terms of the competition," he said.
"It is a fantastic competition and has great history and tradition, there is no doubt about that. But if you're in a position where we are and with the injuries we have there is only one major priority at this football club from all levels.
"From all levels, I mean from the owners all the way down, that priority lies with the Barclays Premier League and that won't ever change for any football club, irrespective of who they are.
"At this stage of the season, when we face the third round on the back of a heavy, heavy schedule then it becomes less of a priority to all of the other competitions you are involved in, certainly if three days later you have a semi-final against Manchester City up at the Etihad Stadium."
Allardyce is ready to give the acid test of first-team football to a number of his youngsters on Sunday with an injury-ravaged squad, made worse with the absence of suspended captain Kevin Nolan.
There is no doubt the West Ham team that lines up at Forest will be quite different to that which is fighting for Barclays Premier League survival at present.
Allardyce has just 14 fit first-team players and has already said he will include at least seven of his Under-21 squad in the group which travels to the east Midlands.
"It is backs to the wall at the minute as far as players available are concerned for the games that are coming up," he said.
"We have to roll with what we've got and, with the games coming as thick and fast as they are, a lot of the younger players will now be escalated into the first-team level to see if they can master the challenge and show us what they've got in terms of ability, starting at Nottingham Forest on Sunday."
The 59-year-old has been in the game long enough to know blooding his younger players is a doubled-edged sword with regards to the possible backlash from the club's fans.
Allardyce said: "Everyone says 'when are you going to start playing your youngsters?' so we're going to start playing them. If we don't win, they'll say 'he's undermining the FA Cup', so here I am in a no-win situation.
"We had one or two little digs before we played Tottenham in the Capital One Cup about the team we were going to play and we won. My job is to put the best available team out, bearing in mind what I've got after that and the injuries I've got."
With Andy Carroll, Mark Noble, James Collins, Winston Reid, James Tomkins and Ricardo Vaz Te all sidelined, any young players will have a chance to earn a place in the first-team squad for the coming weeks.
Goalkeeper Jussi Jaaskelainen is likely to be rested as Adrian once again deputises and the experienced Finn feels that, with two cup ties to play before their next league fixture, the squad can be stronger and ready to battle for survival sooner than otherwise possible.
"You just need to approach the next game and leave everything behind you," he told the club's official website.
"The only thing you can control is the future. Maybe it is a good thing with the injuries we have at the moment. It gives us a little bit more time for the boys to recover and obviously it is good for our skipper that his suspension goes through the cup as well."