Carroll, who joined West Ham on loan from Liverpool, made an impressive start as he teamed up with Ricardo Vaz Te to set up Kevin Nolan for the Hammers' first-minute opener in a 3-0 win over Fulham.
However, Carroll was substituted in the second half - and Allardyce revealed afterwards the 6ft 3in striker may have suffered a hamstring injury.
The West Ham boss told Sky Sports 2: "It's a huge result but the only real disappointment for us is Andy might have tweaked a hamstring.
"It is hugely disappointing if that's the case...but it will be unlikely he goes (away with England).
"I don't think he's much chance - sadly for Roy (England manager, Hodgson) and sadly for us. It depends on the extent of the damage.
"He is desperate to play football. We had Carlton Cole warmed up and ready to go and Andy was going to be substituted anyway in the next couple of minutes.
"But unusually he did it (injured the hamstring) on the jump."
Allardyce added: "No question it's the right result. Fulham were out of sight by half-time and that doesn't happen too often with a newly-promoted side finding their feet in the Premier League.
"We don't want Andy's injury to detract from our performance. For that first goal there is flicking the ball on and knowing where the players are running. Vaz (Ricardo Vaz Te) knew if he got in that position it was a ball Andy could flick to him."
Fulham boss Martin Jol acknowledged his team did not get to grips with the threat of Carroll.
He said: "You have to be on the end of the first balls or get on the end of the knockdowns - and we didn't do that, although we were better in the second half.
"We had four or five players who lacked a bit of rhythm because of transfers. Hopefully we will get a bit of balance in the next month."
Nolan believes the Hammers' activity in the transfer market helped them make a flying start.
Allardyce was busy in the transfer window, with loan signings Yossi Benayoun and Carroll the final additions.
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Nolan told Sky Sports 2: "Signing Yossi gave all the lads a lift and I think you saw that today [Saturday] and Andy is a great lad - we get on really well off the pitch.
"When we knew he was coming down on Thursday I was excited and really chuffed. We've been so lucky to get him and we're delighted for him because he deserves to be played every week.
"We all know his capabilities. It's disappointing what went on at Liverpool I think but he's showed he's a top player in this league and hopefully he can get some goals for us.
"An early goal helps settle the nerves and means you can put your game-plan into action.
"We all knew we'd be getting players in and we're delighted with the quality of players who have come in."
Nolan was delighted with the response to last week's 3-0 defeat at Swansea, with Winston Reid and Matt Taylor getting the other goals.
He added: "After the disappointment of last week it was important we bounced back.
"We were confident going into the season but it's back to the drawing board now. It's nice to go into an international break having done the business.
"Overall it was a fantastic afternoon and we are very happy with the three points."