The former Labour leadership contender told the Acting Prime Minister podcast that the 2016 Brexit referendum "put the British public into an impossible position" and she wishes she voted against it in the Commons, rather than abstaining.
Asked by podcast host Paul Brand whether she believes she should have voted for former PM Theresa May's deal, which would have resulted in a 'softer' Brexit, the senior Labour MP disagreed.
She said: "The big mistake I think I made, to be honest, was voting for that referendum without any kind of safeguard or guarantees.
"I didn't actually vote for it because I didn't agree with it, but I should have voted against it.
That's one of my biggest regrets. I abstained in the end out of deference for the party, and I argued against it, but I just think we put the British public into an impossible position.
"And when we got the result, it was obvious that all we'd done was managed to bring to the surface huge divisions that were not going to be easily resolved."
Ms Nandy said there's "absolutely no reason" why Boris Johnson should not be able to reach a free trade agreement with the EU, but wouldn't give her backing to a deal before she's able to see it.
She appeared to acknowledge difficulty in negotiating a deal, saying the EU's opening position on fisheries and level-playing field regulations "was unreasonable".
"If we'd been in government, I would have been pushing very hard for us to push back on that and say to the EU, come on, you need to move closer to us and you need to compromise."
But Ms Nandy says the difference between the UK and EU position is now "ideological" and a breakthrough should be found.
When asked whether she'd support a free trade agreement in any form over a no deal outcome, the frontbencher said she could only vote one if she could be sure it did not have an impact on the Good Friday Agreement.
She said it is starting to look like "there may be nothing to vote for at all".
"That would be a disaster," she added.
Listen to the podcast here: