Lambert enjoyed a dream debut on Wednesday when he scored the winner in England's 3-2 victory over Scotland at Wembley with his first touch in international football.
Allardyce hailed Lambert's contribution as "Roy of the Rovers stuff" and believes the 31-year-old has emerged as a genuine competitor to Carroll, who is currently recovering from an ankle injury.
"I think there a choice for that type of player between Andy and Rickie. It's going to be a challenge this season on who's the best of the two," Allardyce said.
"Andy is looking forward to playing for us and doing a great job, which we would hope will get him to Brazil. I'm sure Rickie is the same. One or the other would go.
"I think it will be a competition between the two on who consistently plays the best this season. From a selfish point of view I hope it's Andy.
"But for Rickie it was great to see him come on and make a statement. To get the winner against Scotland shows what he (Lambert) can do and what England might be missing a bit.
"That's when they get into the final third and a crowded penalty area, and the best way of penetrating that type of defensive situation is aerially; he is a very strong, powerful header of the ball.
"It shows you have to have other dimensions in your squad no matter what level you play at."
Allardyce hopes the signing of winger Stewart Downing from Liverpool can bring the best out of former Newcastle frontman Carroll.
"As everyone knows I like crosses and there are lots of managers who don't like (crosses) any more," Allardyce added.
"Stewart is a quality player, value for money; somebody who sits at the top of our performance stats as well as a nice guy."