The teams face each other in the Premier League on Saturday, and the Frenchman sees the England international as a key player for the home side.
However, he insists his team will focus solely on themselves when they travel to east London for the game at Upton Park.
"Carroll has the quality and that will come out with time. We expect Carroll to be at his best - it is down to us to deal with that," Wenger told reporters.
“We can only focus on our own performance and be at our best.
"He started very well, then he had to deal with a high level of expectation with a massive transfer on his shoulders going to an historic club where a lot was expected of him. Maybe it was a bit too early for him.
|MORE TO COME FROM CARROLL - WENGER
|7/1||Andy Carroll is 7/1 with bet365 to score the final goal in the West Ham v Arsenal game
The 62-year-old went on to praise the Hammers, insisting there is more to their game than the physical style of play favoured by manager Sam Allardyce.
He said: "West Ham have a good balance, they are efficient, they are a good mixture I must say between direct play and playing on the ground.
"Technically they are quite sound in midfield, they have Carroll and [Carlton] Cole up front who can go for high balls.
"We know we will have a big challenge there, we know we will only get away with the points if we perform at our best.
"Allardyce has again a very good team and you have to give him credit for that.
"He has built a good team, well balanced, always efficient and he is a good manager because he lasts."
After a recent spate of controversy regarding refereeing decisions, Wenger expressed his belief that players should stop harassing officials after decisions have been made.
"It is down to the referee to make the right decision," he added.
"Once he has given a penalty, once he has given a goal, who was offside, [the referee] will not come back on his decision anyway.
"The press has made, and rightly so, campaigns that the players should leave the referee alone.
"Sometimes you question yourselves, when the other teams do it and your players don't do it, that you have a little disadvantage, but I don't think it can be a rule for us to encourage our players to do that.
"We should leave the referee as much as we can alone to make his decisions."