The Hammers saw a prolonged appeal against Carroll's dismissal against Swansea rejected late last week, leaving Allardyce once again without the services of the England international.
Carroll had featured in just four matches before his red card, after struggling to overcome a troublesome foot injury.
While Carroll was out injured the Hammers looked doomed to a season fighting relegation but, with skipper Kevin Nolan once again leading the way, Allardyce has his side back on track.
Now they face Norwich at home on Tuesday night and also welcome Southampton to Upton Park during Carroll's suspension.
But for Allardyce, who gave fellow strikers Carlton Cole and on-loan Marco Borriello equal chance to prove their worth at Villa, a scenario which saw Carroll not coming straight back into the side would be welcomed.
"What about this?," Allardyce said. "Andy Carroll comes back from suspension, West Ham haven't lost a game and won most of them and Andy Carroll has to sit on the bench. That would be nice.
"Carlton and Marco played a dual role (against Villa) - 45 minutes apiece - which is what I talked to them about before the game.
"I told them 'today will be 45 minutes each for you so give us your best 45 minutes to help your team try and win'.
"Both made a contribution on Saturday and they will have to continue to do so."
Meanwhile, Norwich manager Chris Hughton thinks Hammers captain Kevin Nolan could pose as much of a threat as Carroll.
The Canaries head to east London on the back of a morale-boosting goalless draw with title chasing Manchester City on Saturday, but only two points clear of the Barclays Premier League relegation zone.
West Ham are a place above in 15th on goal difference having hauled themselves out of the bottom three with the win at Villa.
Nolan - just back from a recent ban himself - grabbed his second double in as many games against Swansea to help drag Allardyce's men up the table.
"It is about team performance and what West Ham have shown is that when they have looked for a goalscorer or a bit of inspiration, then Kevin Nolan has come up trumps for them, and that is the type of individual he is," said Hughton, who could have Scotland winger Robert Snodgrass back from a groin injury.
"When you look at team selection, there is always something that can hurt you, for somebody who does not play, it is an opportunity for someone else.
"You can only play against the team you are up against, and prepare yourself for what their starting XI might be, but also have ambitions to win the game yourself."
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