Fulham had been by far the better side until three minutes before half-time when West Ham scored against the run of play through Carlton Cole.
Zola said: "I don't know if we were lucky today, I will leave it up to others to judge. But when you win you need a little bit of luck. Certainly I am not one who regrets luck.
"I would like to have luck in every single game but we played a good match and had a few occasions in the second half to make it (the scoreline) bigger. I would like to be lucky every Saturday.
"I have been working with this team for two weeks and they know what kind of football I want. They are doing very well and they will get much better.
"Winning away games like this will give them a lot of confidence."
"I thought we played some excellent football but within three minutes, a game we looked like being able to win and certainly give a good account of ourselves, within three minutes everything changed.
"I as really amazed how the players in the second half showed their character and physical fitness to work as hard as they did and almost bring us back into the game.
"Unfortunately at this level of football, when you are two goals down it is not easy to come back, especially when you have 10 men rather than 11."