The former Labour leadership candidate acknowledged Labour’s three-line whip on supporting Article 50 meant the party would be to blame if the vote to activate Article 50 goes ahead.
Mr Smith, who has repeatedly criticised Jeremy Corbyn and the Labour leadership, has made clear he will vote against triggering Article 50, despite his constituency voting leave.
The MP for Pontypridd was asked on BBC Daily Politics whether opponents of Brexit had a genuine chance of forcing the government to abandon the process.
He told Andrew Neil: "I am not anticipating we will be able to stop Article 50. There is a majority in the Commons, in the Labour Party and in the Tory Party to get that passed.
“The right thing for me to do, and the right thing for Labour to do is to stand against it.”
Owen Smith admits Labour would be to blame for passing of Bill
I appreciate I’m in a sizeable minority on that point
Neil then said: “The reason why the Government can bank on a clear majority on Article 50 is because your party has imposed a three-line whip to vote for Article 50.
“If it gets through Parliament without even being scratched on the way that will be down to your party.”
“Yes,” replied a clearly embarrassed Mr Smith said.
The interview took place shortly before it was announced that Jo Stevens had resigned from the shadow cabinet in protest at Mr Corbyn's stance on Brexit.
The Labour leader faces a growing rebellion after imposing a three-line whip requiring his MPs to back the Bill allowing Theresa May to trigger Article 50.
Cardiff Central MP Ms Stevens quit as shadow Welsh secretary, becoming the first member of Mr Corbyn's top team to resign over the issue.
She follows shadow education minister Tulip Siddiq in quitting, while two whips – supposedly responsible for party discipline – have indicated they will also rebel and risk being sacked.
Ms Stevens said: "Theresa May is now leading our country towards a brutal exit with all the damage that will cause to the people and communities we represent."
Blair and Juncker: Together through the years
Wed, January 25, 2017
Former Prime Minister, Tony Blair and President of the European Commission, Jean-Claude Juncker have always shared a friendly relationship over the years.
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EU Commission President Juncker greets former British PM Blair in Brussels
Brexit Secretary David Davis has presented the European Union (Notification of Withdrawal) Bill to the House of Commons.
It is expected to move through Parliament before Theresa May's deadline of March 31 to trigger Article 50.
Jeremy Corbyn’s party have announced they will table nine amendments to the proposed legislation.