Thomas Vermaelen was sent off in the first half of the game after brining down West Ham star Guillermo Franco in the box, but Manuel Almunia saved the penalty kick.
“I am disappointed, especially after the first half when I thought that we were playing the best game of the season,” Zola said.
“The key was to keep the discipline because you have the extra man and I told them to keep it simple, to move the ball around until we have two versus one.
“We did it for the first five minutes of the second half, but then lost it. We wanted to sort the game out as individuals. You can’t think like that.
“With Arsenal, you can expect it will be difficult, even if they are one man down.
“Scoring the penalty would have been a big help because Arsenal would have played different football.
“But they just sat back and played the counter-attack. We just did not use the extra man.”