Zamora completed a move from Upton Park to Fulham earlier this week in a £6.3million joint deal with defender John Pantsil.
The 27-year-old striker is not sure why West Ham let him leave but is determined to show his quality at Craven Cottage.
"I don't rate Deano miles ahead of me at all. I really don't think he's any better than me particularly," Zamora told the Daily Star Sunday.
"I've scored more goals than him as well but that's football I suppose.
"I don't think it was an age thing. I'm only 27 and you're supposed to be in your prime then, aren't you?
"I think it was just one of those things. The club needed the money and there was a bid on the table.
"Maybe nobody came in for Deano."