The Hammers climbed into sixth place with Sunday's 1-0 victory at Newcastle, a club at which the three men have enjoyed differing fortunes in the recent past, with Nolan's fifth goal of the campaign securing the points.
Allardyce said: "Kevin's relationship with Andy is such a good one that I don't need to do a lot of coaching with those two. Kevin will instinctively play off Andy and vice-versa. While Andy is struggling to get a goal - and we would like him to get one - Kevin is the man who is scoring the goals because that combination is causing teams lots of problems."
He went on: "We have a strike-force there that is reaping rewards for the team by winning games of football, and 18 points after 11 games for a newly-promoted side is an outstanding start."
Carroll is still waiting to open his account at Upton Park and was denied by former team-mate Tim Krul 18 minutes from time on Tyneside as the visitors hit the Magpies on the break amid a concerted second-half assault.
Allardyce said: "He is getting better and better as time goes on, and that partnership with Kevin is vital for us. it's a brilliant partnership. Long may it continue. It's getting us victories, it's getting us points."
But ultimately, they were unable to produce the kind of quality which served them so well last season and with the Hammers defending determinedly, they made it to the final whistle without mishap.
He said: "We lacked a bit of power on the pitch. It was a game for Tiote, really, and unfortunately we didn't have him available today. That sending-off has proved costly for us because it has cost us three points today."