Carroll is back in the spotlight after scoring twice in three games and causing problems for Manchester United with a physical display which, in Sir Alex Ferguson's opinion, should have brought a red card.
Martinez, whose side will start the weekend in the bottom three following their midweek defeat at Manchester City, said: "We all saw the power Andy Carroll brings.
"The way he attacks the ball in the final third - as he did at Newcastle - is quite unique and the best in the business.
"Now he is doing that for West Ham and is becoming very important for them and they are getting the best out of the player.
"If you can allow him to get the best out of his strengths he is going to enjoy his football and will be very powerful for the team. At the moment he is in full flow."
Wigan competed with champions City for long periods at the Etihad, and Martinez said: "It was a very positive performance.
"Yes, at this stage of the season we need the points and to get the results but if you look at the dressing room it is full of confidence.
"When I see us visiting the champions and, in the game, demanding three points that fills me with pride because it shows how far we've come. We are prepared to go until the last ball is kicked on May 19."