Hammers striker Carroll is hoping to force his way back into Roy Hodgson's Three Lions squad in time for this summer's World Cup in Brazil.
And the 25-year-old, who has made only seven appearances this season due to injury and suspension, looked like a man on a mission on Saturday as he netted his first goal of the campaign in the fifth minute of his side's Barclays Premier League match at Stoke.
It was a trademark effort from the tall frontman as he outjumped his marker - the even taller Peter Crouch - to crash in a header, and although West Ham eventually lost 3-1, he frequently looked a threat during his 83-minute run-out.
And asked about Carroll's World Cup prospects and whether there is still a place for that sort of player in international football, Allardyce said: "Headed goals can never go out of the game.
"Anybody that tries to take headed goals out of the game destroys the game as an entertainment, diminishes the entertainment value.
"Andy is one of the best headers of the ball you will find, which he showed in the Stoke match.
"And not only did he head the ball in the net, he had some of the biggest defenders in the game against him and they couldn't cope."
Certainly, the World Cup is in the thoughts of Carroll, holder of nine senior England caps, with the last coming in 2012.
Asked if Brazil was on his mind, Carroll said: "Of course it is, yes.
"Obviously I am thinking about that, but I have to keep scoring goals for West Ham and we have to start winning games again before that comes."
Allardyce felt Carroll, West Ham's record signing, had caused such problems for Stoke captain Ryan Shawcross that the centre-back had been forced to resort to "persistent fouling".
The manager said: "Shawcross fouled him six times, that's how much trouble he was causing him.
"We are disappointed the referee (Craig Pawson) didn't book him for persistent fouling."
Allardyce was also disappointed that what he regarded as a "blatant" handball in the home box by Stoke defender Marc Muniesa had not prompted Pawson to award the visitors a penalty.
The ball struck Muniesa's arm as he jumped in front of Carroll to beat him to it.
Carroll said: "The ball was coming into my chest and I feel like I would have brought it down.
"I thought it clearly hit his hand, but obviously the ref didn't."