Tom Watson said he feared the results of the European elections would show voters had deserted the party and blamed Labour's ambiguous position on a public vote.
The party must stop "hedging its bets" and urgently re-think its stance in order to realign itself with its members, he added.
Writing in The Observer, he said: "For our party's sake, but most of all for Britain's sake, Labour needs to find some backbone on Brexit, find our voice - and do it fast."
He added: "Our performance (in the European elections) is a direct result of our mealy-mouthed backing for a public vote on Brexit when it is being demanded loud and clear by the overwhelming majority of our members and voters.
"Polls show Labour has been losing up to four times more voters to parties giving full backing to a people's vote than to Farage. And those same polls show we would have beaten him by a country mile if we had unambiguously backed a public vote on any form of Brexit.
"Once results are in, we must channel our frustration into winning those voters back. Never again can Labour policy on the most crucial issue of our generation be on the wrong side of its members and voters."
Mr Watson described the party's stance on a second referendum as "a deliberate, self-defeating attempt to triangulate between different groups".
Ahead of the European elections, Jeremy Corbyn saw off an attempt by pro-EU members to commit the party to a confirmatory referendum on any Brexit deal.
The party's ruling National Executive Committee agreed its manifesto would instead stick to the wording of a motion passed by Labour conference last year, which keeps a public vote on the table as a last option.
This decision was made by a "small number of people" and should instead be made by party members, Mr Watson said.
The deputy leader also vowed to support calls for Labour's Brexit policy to be changed before the autumn party conference.
"I fear that unless our policy on Brexit changes we will not have the opportunity to be the radical reforming government that so many millions of people in our country need," he said. "The campaign to change that begins now."
Additional reporting by Press Association.