"At that stage [51-3] it looked like England were getting themselves back into this game at a rate of knots," said Broad.
Broad concluded that New Zealand's current advantage allows them to dictate the pace of the upcoming fourth day.
"Now, with New Zealand leading by 204, they're in their changing room going 'look guys, we get another 160, 170 with these final seven wickets, we can put this game to bed'," he said.
The commentator also recalled previous successful chases at the venue, such as a 299-run target achieved against New Zealand four years ago under Ben Stokes.
"You think about those famous chases - here, Headingley [358 against Australia in 2019], Edgbaston [378 against India in 2022] - none of them had this variance of bounce, but the England mindset will be that 'we can get these runs'," said Broad.
He noted that the rapid outfield conditions at Trent Bridge could benefit the batsmen if the opposing bowlers falter.
"We know Trent Bridge is a famous white-ball ground as well, where there's been a lot of high ODI scores and a rapid outfield," said Broad.
Broad credited the tactical performance of the visitors' bowling attack on the third day.
"New Zealand bowled very well today.
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They didn't bowl so well yesterday afternoon, so you just have to hope that a relatively inexperienced bowling line-up turns up and you can score runs," he said.
