The Shadow Chancellor was among the 18 Labour MPs, 283 Conservatives, eight DUP and two independents who defeated an amendment pushed by party colleague Ian Murray.
It came as MPs considered resolutions linked to the Taxation (Cross-Border Trade) Bill, which aims to put in law a new post-Brexit customs regime.
MPs heard the Bill will pave the way for domestic legislation that will enable the UK to charge customs duty on goods - including those imported from the EU - and outline how customs checks will be made.
Labour former frontbencher Mr Murray's amendment sought to exempt EU goods from the new regime, and was supported during the vote by Tory rebels Anna Soubry and Ken Clarke.
But speaking ahead of the vote, shadow Treasury minister Anneliese Dodds said Mr Murray's proposal could - as an unintended consequence - "worsen our situation".
Mr Murray said: "Can I just say to her if she disagrees with the technical aspects of my amendment, but agrees with the principle of staying in the customs union, where are the frontbench amendments to do that?"
Ms Dodds said the Labour position remained to "keep all options on the table", adding: "Ultimately we are seeking to have a more democratic process, we aren't able to vote on that which is unfortunate.
"I think he will know that ultimately, as I stated before, the Labour position is to leave all options on the table and that is the best thing for Britain to be doing.
"It is very, very unfortunate that the Government side have failed to do that because it is enormously damaging for our negotiating position.
"I very much regret that the Government still could irresponsibly and recklessly lead us to a no deal scenario and in that case these amendments sadly would worsen our situation, I know that is not intended by the proposers, quite the opposite.
"I'm afraid that is what technically they would lead to."
Mr Murray's amendment was defeated by 311 votes to 76, majority 235.
Shadow International Trade Secretary Barry Gardiner, Ms Dodds and shadow Treasury colleagues Peter Dowd and Jonathan Reynolds were among the Labour MPs who voted against the amendment.
The vote came after a debate which saw Mr Murray speak in support of remaining in the customs union.
Former minister Ms Soubry added: "It can't be right that the overwhelming majority of honourable and right honourable members in this place agree that we should be in the customs union and the single market.
"And the only reason that that isn't even on the table anymore, and it's an uncomfortable truth, is because I fear my party is in hock to 30 to 35 hard, ideologically driven Brexiteers."
Treasury minister Mel Stride earlier also acknowledged that major problems will be caused at Dover if the post-Brexit customs checks system stops for more than a couple of minutes.
But Mr Stride said the Government is placing an "extremely high priority" on making sure the UK's roll-on, roll-off (ro-ro) ports continue to "move effectively".
He added he is "confident" the required customs arrangements will be in place to "keep the traffic moving on day one".
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