Barnett, 37, who has been the presenter of the Radio 4 show Woman's Hour since January 2021, also said her friends and family are not always pleased with her slipping into 'host mode' in social situations.
Like Paxman, Barnett is known for her relentless and insightful interviewing, and was reminded by Kate Thornton on the White White Question Time podcast that Paxman had once called her 'his favourite interviewer.
The broadcaster said: "He did say that, which was very nice, and [I'm] very appreciative. I think people always want to compare you to somebody, so that then did lead to those sorts of comparisons.
"But I feel quite happy about the fact I've always been how I am. I'm not modelling myself on him."
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Barnett said she had interviewed Paxman twice, once at a literary festival and once during her time on BBC Radio 5 Live, where she worked for six years.
Thornton described it as 'quite the compliment coming from quite the Rottweiler'.
Barnett also explained she never went into an interview with an idea of how it might go, or that it might end up being a viral moment, such as in 2017 when Jeremy Corbyn could not answer her questions on the costs of a proposed childcare offer.
She said many people who thought of her as a 'hard interviewer' probably didn't really know what she did or about her range of work, and that the many years she had been working in TV and radio had helped her to 'find her voice'.
"When my interviews, or clips of them, have gone viral, those things only escalate in response to the person potentially not answering. It's never the design," she explained.
"You always are onto a losing ticket if you go into an interview and think: 'I'm going to do this'. You have to go in curious and you have to try and go in humble."
She said the most important thing she had learned as a journalist was the need to listen, be well researched and to not rely too heavily on a plan.
"Everyone's got a plan until they get punched in the face," she said. "Then that's the end of that part, that interview is just not happening because now we're doing this.
"So you can't always do any planning at all. But if you feel good about the research, at least you can go where it goes."
Barnett also said her husband, who she met at university, had to ask her not to go into 'host mode' in social situations, while she admits she likes to help when people 'can't tell their own stories very well'.
"I think I did frighten one of my friends recently," she told Thornton, "when I did mention that if I think something's getting quite dull, I might spice it up with something, socially.
"And she said: 'We can all tell when you're doing that, and we wish you wouldn't.'"
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