Ms Thornberry also ruled out Labour would support calls for a second Brexit referendum unless a large majority of Britons asked for it.
She said: “As for a second referendum if 90 percent of the population was saying ‘we must stay in the European Union, we must not leave’ that would be a challenge for all of us democrats.
“At the moment we proceed in good faith, we do as we are instructed and we are leaving the European Union. We must respect the results of the referendum which means that we have to leave but we have to look after the economy which in my view means that we don’t go very far.”
She Shadow First Secretary of State said her party had to balance members’ demands and the will of the British people to leave the European Union.
She added Labour will seek to protect jobs and the economy while supporting the British Government deliver Brexit.
Ms Thornberry told the Andrew Marr Show: “When we are developing policy we have a responsibility to have deep respect for our membership but also for our country as a whole.
“I have a responsibility to be a representative for Islington South and Finsbury, who want to remain in the European Union when the country wants us to leave. It is a difficult balancing act.
“We have to keep the Government honest and we have to make that when we do leave we are making decisions that actually look after our country which means look after jobs for our kids.”
It comes after Shadow Brexit Secretary Sir Keir Starmer warned Labour would vote against the Government’s Brexit bill if it failed to meet his red lines to ensure Britain remains commercially close to the European Union.
Speaking at a meeting of the Fabian Society, the Sir Keir said: “If what comes back does not provide for a strong and collaborative relationship we’re not signing it. We’re not voting for it.”
His red lines include remaining as close as possible to the bloc’s Single Market and the Customs Union, the defence of rights currently provided by the union and “a humane, effective, immigration approach”.
Sir Keir’s other red lines included “a strong and collaborative future relationship” with the EU, effective measures to handle terrorism and national security and a deal which “delivered for all regions and nations of the UK”.
He added: “The way the Government is going at the moment, it has a long way to go before it gets anywhere near our tests.”