"People don't realise how young we are," the Frenchman said. "This team will win but the sooner the better and we can win this year.
"We have improved on the maturity side. We played with class and spirit and kept our nerve in the important moments which will only strengthen our belief in future games."
Few doubt that Arsenal have the talent in their ranks to win the league and Wenger played down doubts about the ability of his young team to cope with the mental pressure.
"We are not under any special pressure because we are beyond expectations," Wenger added. "We are all conscious we've won nothing yet but the hunger is there, the talent is there and that means nerves are there."
Wenger's men looked to be comfortable after Brazilian midfielder Denilson scored with a sweet low shot after five minutes, but were jolted just before half-time when defender Thomas Vermaelen conceded a penalty.
The Belgium centre-back was red-carded after hauling down Mexico winger Guillermo Franco in the box, and will now serve a one-match ban.
West Ham winger Alessandro Diamanti took the spot-kick but was thwarted by Arsenal stopper Manuel Almunia's full-length save to his left.
Captain Cesc Fabregas, returning after a two match absence, sealed the points late on, converting a penalty after defender Matthew Upson handled in the area.
Vermaelen's suspension exposes Arsenal's lack of cover in central defence but Wenger backed Cameroon midfielder Alex Song to shine after turning in an assured display in defence when asked to drop back after the red card.
"Song was absolutely outstanding, it looked so easy to him," he said. "I know he can play there and I have no fear to continue playing him at the back."
The north-London team have drawn favourites Barcelona in the Champions League and they will need the experience of veteran defender Sol Campbell and Saturday's hero Almunia if the season is not to peter out.
Wenger expressed concern over the workload of his centre-half, but backed his Portuguese stopper to continue confounding his doubters.
"He (Almunia) made a few errors at the start of the season but for two or three months he's been absolutely outstanding and credit to him. He is silencing his critics," the Frenchman said.
"Sol was outstanding but to repeat games could be a problem. He's very important to us and his experience is vital in the dressing room. He's done it before so the players listen to him."
The Hammers sit just three points above the relegation zone but showed enough class and fight on Saturday to suggest they should stay up.
Italian manager Gianfranco Zola stressed the importance of the coming week in their survival bid. The Iron entertain fellow strugglers Wolverhampton at Upton Park on Tuesday before Stoke visit next Saturday.
"Tuesday and Saturday will tell us a lot," Zola admitted.
"There doesn't seem to be a loss of confidence. We played one of best teams in Europe and played very good football. We go into the game in good shape."
The former Parma player backed counterpart Wenger's assertion that the Gunners were strong enough to win the league.
"Today was a very mature performance from Arsenal," the former Chelsea man said. "They sat back and countered very well and I was very impressed with Song. He played fantastically," he added.