Premier League Preview: Liverpool v West Ham
Allardyce's men head to Merseyside on Saturday hoping to preserve their position ahead of Liverpool in the Premier League table.
Seventh-placed West Ham hold a one-point advantage over Brendan Rodgers' side following a first half to the season that exceeded expectations.
This weekend's fixture marks Carroll's first return to Anfield since joining West Ham on an initial loan deal that became permanent in May 2013, and Allardyce has urged the striker to play his own game.
"I hope he doesn't try too hard because that can put you off your game," he said. "But football is a team game, so we want everyone to do well and help each other out.
"I'm sure Andy would like to score and we'll certainly do what we can to try and help him do that. I certainly don't think he has anything to prove, everyone knows how good he is.
"He just needs to focus and prepare like he does for every game, keep a calm head and play his normal game."
Carroll, who will be joined by Stewart Downing in facing his former club, has hit form since returning from an ankle injury - scoring five goals in 12 league appearances.
But Rodgers has no regrets about letting Carroll leave, insisting the towering frontman - who scored 11 times in 58 outings in all competitions after his big-money move to Liverpool from Newcastle United - would have seen opportunities limited.
"I felt in terms of how I play and how the team has operated over a couple of seasons, he would not have been a regular here," he said.
While West Ham are reaping the benefits of having their in-form English striker fully fit, Liverpool continue to patiently wait for Daniel Sturridge's comeback from a combination of thigh and calf injuries.
Sturridge could be in line for a return this weekend, although Rodgers says he will not gamble with his fitness.
"We have to be careful with him as he's been out a long time, but to have him back for the second part of the season will make us a better team," Rodgers said.
"In the last few days, and in particular this morning [Thursday], he was brilliant in training - really back to what we had seen before. I can tell he is happy and feeling very strong in his own body."
Liverpool have question marks over the fitness of Mamadou Sakho (knock), while Alex Song, James Tomkins, Carl Jenkinson (all "knocks and bruises" according to Allardyce) and James Collins (back) are doubts for West Ham.