The 25-year-old former Newcastle frontman headed the Hammers into an early lead at Sunderland and turned in a fine individual display as Allardyce's men ran out 2-1 winners at the Stadium of Light.
Victory on Wearside left the men from Upton Park 11 points clear of the drop zone with just six games to play, but left Carroll with a new target ahead of him.
Asked if there was enough football left for the frontman to force his way into Roy Hodgson's England squad, Allardyce said: "I think there is.
"There are six games to go and I think if he continues to score, if he scores anything like he did last season - he scored eight in the last 12, I think - if he gets another two or three or four goals, I think it will hopefully be difficult for Roy to ignore him.
"There are not a lot of them today, unfortunately. I used to play against them every week, Andy Carrolls, when I played many years ago. There used to be one in every side
"But there's a quality with the size and the stature of the man. It's not just a heading ability, it's an all-round quality that he has.
"He's quicker than he looks, some good hold-up play off the chest at times, takes the ball with his feet, he's got a terrific shot on him.
"He's superb in the air and he's young, so hopefully he keeps on not growing stature-wise, but growing in terms of his experience and his ability to stay fit and be an even better player than he already is."
The Hammers looked to be cruising when, after Carroll had headed them into a ninth-minute lead, Mohamed Diame doubled their advantage fives minutes into the second half.
However, substitute Adam Johnson gave Sunderland, who saw strong appeals for a first-half penalty turned down, hope when he pulled a goal back 25 minutes from time to prompt a late assault.
But although Ki Sung-yueng, Connor Wickham, Fabio Borini and substitute Ignacio Scocco went close, the visitors held out to all but secure their own top-flight status.
Allardyce, who was booed by his own club's fans after last week's 2-1 victory over 10-man Hull, was a satisfied man as he left the north-east.
He said: "We have won six of the last nine matches, we are probably in the top four or five in the Premier League for results at the moment.
"It got us out of trouble and it's got us almost safe - not quite mathematically, but I think it would be difficult for anybody to catch us now."
By contrast, opposite number Gus Poyet cut a disconsolate figure as a must-win game ended in a defeat which left his side four points adrift of safety with eight games to play.
However, he remained defiant as he considered the task ahead.
He said: "Look, if my team gives up, I will leave. Nobody will need to sack me, I will leave on my own, so if you see this team giving up before the end of the season, you won't see me here."
Sunderland have now won only one of their last nine home league games and taken just a single point from the last 18 they have contested.
Asked if the Black Cats could stay up, Poyet said: "Well, if we play like we played against Liverpool and today in the next eight games, we are going to have a great chance.
"Now the crystal ball, I can tell you, is not in my house, so I am not going to try to read the future because I'm not very good at that."
Hammers boss Sam Allardyce is certainly of the opinion that Carroll should go to Brazil.
"If you want alternatives, Andy gives you one," he said.
"He's unique in many ways. Not many can receive the ball and head a ball as good as he does, especially with quality balls in the box.
"Nobody was going to stop him for that goal. He has a lot more on the deck than people give him credit for. If he plays every week, scores goals, hopefully he'll go to Brazil."
Allardyce has survived some tough moments this season and he feels his club are feeling the benefit of sticking with him and not changing managers like so many of their rivals.
"I think so," he said when asked if stability had helped.
"From our point of view, the chairmen have always been solid and never made me feel under any pressure. We've had an eight-game run and got 15 points, which is fantastic at this stage of the season. It's got us out of trouble and we will now strive to see how many more points we can pick up."
Beaten manager Gus Poyet said: "It's difficult to accept, sometimes when you see a team at the bottom they have no spirit, heart and give up.
"I don't think it's possible to see my team giving up.
"The downside of the game (is the defending) and we knew that was the way they could hurt us. We will have a few chats about that."
Poyet felt his men had been worthy of a penalty when Nolan appeared to elbow the ball in the box.
"It was clear, deliberate. He tried to play the ball with his hand. You would need to ask the referee. It was easy to see but that's the way it's been," he added.
"I hope we get some luck; a decision from the ref or a deflected shot goes in. It's about winning now. We have a chance and will go to the end."