Zola has signed a two-year deal at the club, replacing Sean Dyche, which has led some fans to express their disappointment over the move, having witnessed the former Watford defender guide his side to a relatively respectable 11th place finish.
"Of course I have to [mend some bridges]," the former Hammers boss told The Daily Telegraph.
"I know that the person who was here before me has done very well and to him goes my respect and my admiration.
|AS WEST HAM MANAGER (2008-10)
"He has done a very good job so for me the task will be difficult, but it has always been like that for me. It has always been a challenge since I started playing football.
"I was half of the size of the others and they said I wouldn't stand a chance to become a footballer; I took that challenge and now I have another difficult challenge.
"I told the players I will give everything I have got inside to make them a little bit better and then we will see how the results [go].
"It is interesting. It is a challenge and I take it."
One player the new boss will be desperate to keep is defender Adrian Mariappa, who is currently attracting interest from Premier League new boys Reading among others.
"Adrian I know is a very good player and was one of the best last year," Zola added.
"Obviously we want to keep him but we understand it is not only our decision, also it's Adrian's.
"I understand he maybe has the possibility to go to the Premier League and I won't step in front of him and stop him if he wants to go."