The TV presenter explained that his youngest son Freddy had not taken to the model after they began dating in December.
However, he said that Freddy and his brother Bobby are now dealing with the relationship much better.
"After losing their mum, they don't want another mum," he is quoted as saying in The Sun.
"I reminded Freddy that Nicola isn't trying to be his mummy - that no-one could replace her. That's what he needed to hear and he understood."
The children's mother Jade Goody split from Brazier in 2005 before her death three years ago.
Brazier has recently stated that he is "head over heels" for Nicola T, and that they are planning a possible marriage in the near future.
However, he added: "Nothing really matters to me more than my children."
The presenter recently spoke of his difficult relationship with Goody's mother Jackiey Budden.