But he suggested if Parliament voted to reject any deal struck between Theresa May’s Government and Brussels then MPs could push the decision to a “People’s Vote”.
At the meeting on Thursday night, organised by the Labour Business group, Sir Keir was asked whether things would get worse or whether Brexit could work.
He said: “Yes, things will get worse in the short term, as impact reports show. But I don’t want to tell my kids that it’s all downhill from here.
“We have a duty to make (Brexit) work.”
Asked what would happen if the final deal was rejected, Sir Keir said: “It is Parliament that should decide what happens next, it should have the power to decide the options, and this might involve a general election or a ‘People’s Vote’.”
He added: “We’re not calling for it. We respect the result of the first referendum.
“But we’re not ruling out a second referendum.”
The Unite union, Labour’s biggest financial backer, is also open to the possibility of a second referendum if the Brexit deal is unacceptable.
“We are open to the possibility of a popular vote being held on any deal, depending on political circumstances,” an executive statement backed by the union’s conference said earlier this week.
The People’s Vote campaign, which is calling for a referendum on the Brexit deal, welcomed Sir Keir’s comments.
“Travel inside the Labour Party on this issue is in only one direction,” a spokesman said.
“This week Unite, Labour’s biggest affiliate made it clear that a People’s Vote on the final Brexit deal was a real option for Labour and now the shadow cabinet member with policy responsibility for this area appears to be confirming that view.
“Brexit is a big deal, but it’s not a done deal.”