A motion calling for another poll on Brexit was defeated by a majority of 249, with Mr Austin one of 334 MPs opposing it.
The Dudley North MP, who quit Labour last month, also explained his decisions to back the Prime Minister's Brexit deal and abstain in a vote on delaying Brexit.
He said: "The manifesto on which I stood at the election promised to respect and uphold the result of the referendum.
"I repeated that to people in Dudley, I respect the people I represent and I keep my promises, so I have consistently voted for the Brexit plan, and I voted against having another referendum because I think it would damage truest in our democratic institutions.
"I did not voted to extend Article 50 and delay the process because I think we have to respect the result of the referendum, and I think MPs have to get on with the job we’ve been given because delay is creating uncertainty for business.
"But I am worried about the impact of leaving with 'no deal' would have on manufacturing businesses and the automotive or aerospace industries that provide so many jobs in the Black Country."
As a Labour MP in January, Mr Austin defied the party whip to vote for Theresa May's deal, saying that he did so in order to respect the wishes of his constituency which voted overwhelmingly to leave the EU.
He now sits as an independent MP.