The Hammers climbed into sixth place with Sunday's 1-0 victory at St James' Park, 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.
Sam Allardyce: "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.
"We have a strikeforce 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 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.
"It's our second away win in the Premier League and after our last performance at Wigan, to see us play like this is really pleasing for me because we were dreadful at Wigan and we have turned that around with a really good performance and a great result today."