The England striker, on loan from Liverpool, returned to action following a hamstring injury for the last 20 minutes of Monday night's win at QPR.
Carroll has proved more than a handful for the Arsenal defence before - the 6ft 3ins forward most notably having headed in the winning goal for Newcastle at Emirates Stadium in November 2010.
Wenger, however, warned against focussing too much on the opposition instead of producing the required response when the Gunners look to get their domestic campaign back on track after last weekend's home defeat to Barclays Premier League leaders Chelsea.
"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," said Wenger, who could have 6ft 6ins German defender Per Mertesacker available again tomorrow [Saturday] after a virus.
"We can only focus on our own performance and be at our best."
Wenger continued: "I rate Carroll, and don't think we have seen the best of him until now.
"He started very well, then he had to deal with a high level of expectation with a massive transfer on his shoulders (to Liverpool) going to an historic club where a lot was expected of him. Maybe it was a bit too early for him.
"Since I have seen him at West Ham, he looks back to the Carroll we have seen at Newcastle, that means with less pressure."
Wenger, however, insists the Irons are anything but a long ball side under Sam Allardyce, who guided them back up through the play-offs and to a solid start this season.
"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," he said.
"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."
Wenger added: "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."
While Arsenal may have lost their own talisman striker following the £24million sale of Robin van Persie to Manchester United, the Gunners have still managed to produce plenty of goals through the side.
Gervinho netted his fifth goal in as many games to help Arsenal beat Olympiacos 3-1 in midweek to stay on course for the knockout stages of the Champions League.
The Ivory Coast forward could again be deployed in a central role at Upton Park.
"The thinking was to use well his quality of movement and his pace, but of course you have to overcome a little bit an obstacle that he doesn't correspond well to traditional image you have of a central striker," said Wenger.
"He is not massive, is not a guy who will go for high balls, but he can only try and I must say, he has improved his finishing and it is working very well at the moment."
Wenger has a history of developing widemen into a formidable goal threat.
He added: "I did that with Robin van Persie. He was more a technical player, it was not obvious to put him central striker.
"I did it with Thierry Henry, I did it now with Gervinho and I think I will do it as well with [Theo] Walcott.
"They have other qualities that is well suited to our game - our game is based on movement and technical ability and they have that."