The West Ham striker, on loan from Liverpool, has scored six goals in his last 11 appearances and proved more than a handful for champions-elect Manchester United in midweek.
United boss Sir Alex Ferguson felt the Hammers' front man should have been sent off for flattening goalkeeper David de Gea in their 2-2 draw at Upton Park.
But Martinez insists players have to use whatever strengths they have to their own advantage and will be preparing his defenders for more of the same.
"He is a potent threat and he's always been a threat," said the Latics manager.
"We have seen him at two previous clubs show the same power and strength and he did it for England at the Euros and was very impressive so I don't think it is a surprise to anyone."
Carroll was ushered out of the door at Anfield this summer with almost unseemly haste by Liverpool manager Brendan Rodgers, who did not see the striker fitting into his plan of high-tempo pressing and possession football.
Martinez accepts that all players will not fit into every coach's style, Carroll's specific set of skills can be fully utilised by manager's such as Allardyce.
"Of course there is [a place for a traditional English number nine] but it depends on how you want to play," added the Spaniard.
"There are trends in football and clearly you have seen a huge fashion for the possession football.
"A team like Spain become the most successful team in the world by winning three major tournaments (in succession) and at times they play with no strikers.
"But if you have a team with a very good number nine and you can play in that style it will be effective.
"You have certain strengths and weaknesses as a player and that applies to everyone - even the best player in the world, Lionel Messi, has his weaknesses.
"Sometimes as a player you rely more on your team style to hide those weaknesses or to highlight your strengths.
"We all saw the power Andy Carroll brings and 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.
"I think Andy and has found a very strong connection with Kevin Nolan behind him and he gets good service from the wide areas and at the moment he is in full flow."
Defeat at Manchester City in midweek ended a five-match unbeaten run for Wigan, leaving them three points from safety, albeit with a match in hand.
The Latics were arguably the better team at the Etihad and Martinez said that gave the FA Cup finalists confidence as they approached the final crucial run-in of six league matches.
"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," he stressed.
"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 (when they face fellow strugglers Aston Villa at home)."