The deal, negotiated by Boris Johnson, is due for a review in 2025, which Sir Keir said would be an “important” moment to improve cooperation and seek a closer trading relationship with Brussels.
However, the Labour leader stressed that any Government led by him would not seek to rejoin the customs union, single market or the EU as a whole.
Speaking to the Financial Times on the sidelines of a conference for centre-left leaders in Montreal, he said: “Almost everyone recognises the deal Johnson struck is not a good deal - it’s far too thin. As we go into 2025 we will attempt to get a much better deal for the UK.”
He added: “We have to make it work. That’s not a question of going back in. But I refuse to accept that we can’t make it work. I think about those future generations when I say that.
“I say that as a dad. I’ve got a 15-year-old boy and a 12-year-old girl. I’m not going to let them grow up in a world where all I’ve got to say to them about their future is, it’s going to be worse than it might otherwise have been.
“I’ve got an utter determination to make this work.”
It remains unclear if Brussels would be open to making major changes to the agreement
It comes amid a flurry of overseas engagements before party conference season, with Sir Keir expected to meet French President Emmanuel Macron later this week.
Labour has long been critical of the deal negotiated by the Conservatives under Boris Johnson, with the Trade and Cooperation Agreement up for review in 2025.
The Labour leader earlier said it was “complete garbage" to suggest Labour planned to join an EU-wide migrant quota scheme as part of efforts to tackle small boat crossings in the Channel.
It comes after Prime Minister Rishi Sunak and Home Secretary Suella Braverman accused Labour of planning to let the UK become a "dumping ground" for 100,000 migrants from the EU each year.
The political row emerged after the Labour leader indicated he could be prepared to do a deal with Brussels which would involve the UK taking a quota of asylum seekers who arrive in the bloc in exchange for the ability to return people who cross the English Channel.
“The idea that we’re going to join the EU scheme on quotas is complete nonsense. We’re not an EU member and that wasn’t what I was talking about," he told Sunday Morning with Trevor Phillips on Sky News.
Senior Labour figure Pat McFadden, questioned on the same issue on BBC One’s Sunday With Laura Kuenssberg, said: “I don’t think it’s going to be an allocation of numbers, we’re talking about individual cases where a child may have strong family links here.
“It’s not ‘we’ll take this many, you take that many’ - that’s not the kind of negotiation we want to have.”