"Will I walk away? If the problem is me, why not?" Zola told reporters after the match at Upton Park.
"I will have to think a lot overnight. As far as I can see it is not that the players are not trying enough. They are.
"I have a big bond with the players so it wouldn't be easy to walk out on them. I know the situation is not going the way it should. Obviously, I am prepared to accept the situation.
"We will see what happens. Let me think about it because this is the bottom line.
"I have to see if I am really the right man for the job. I am honest and if I don't see that I am the man I will let you know."
A second-half goal by Stoke substitute Ricardo Fuller consigned the London club to a sixth straight league defeat.
The latest setback leaves West Ham fourth from bottom on 27 points from 32 matches ahead of Hull City on goal difference and just three points above second-bottom Burnley.
Hull and Burnley also have a game in hand.
"It is very painful and I will have to think a lot about how our situation stands and find a solution," Zola added.
"There is a lot to think about. Looking at the results, I can't say I am getting the best out of the players.
"I am not making excuses. We are not performing as well as we should and I take responsibility for that.
"Right now I feel flat because we lost our sixth game in a row. I have to see what is the problem."
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