Zola was forced to look on as a terrible opening 15 minutes saw his side two goals down, while centre-back James Collins was stretchered off injured.
But West Ham responded and got back into the game when Scott Parker scored in the 66th minute after a cross from Jonathon Spector.
It set up a rousing finale and Bolton's nerves were stretched to breaking point by the end of the game but the Hammers were unable to find an equalising goal.
Not only did West Ham lose the points, defender Collins will be out of action for the forseeable future with a hamstring injury according to his manager.
"I do not know how long he is going to be out but it does not look good. He will have a scan tomorrow," Zola said.
Pity"It is a pity that we will lose him for a while as James has been playing well."
Zola felt his side should have got something from the match.
"My only complaint is we did not take the chances we created," he added.
"The performance deserved something more.
"But this is football. You cannot afford to concede to Premier League teams. It is a good lesson for us.
"We were aware the first 15 minutes would be vital as we knew what kind of team Bolton are. So to lose two goals so early in the game was disappointing.
"However they scored a great first goal. He put it right in the top corner and you cannot do anything about a free-kick like that.
"Perhaps we should have done better for the second goal. That was the difference between the teams. No-one will disagree with me that we played the better football."