The prime minister made the comment during a visit to Rwanda, while MPs have been preparing to debate the proposed legislation next week.
On Monday, the Northern Ireland Protocol Bill will be given its second reading in the Commons and MPs will vote on whether it can proceed for further consideration.
The Tory government has argued that the measures to remove checks on goods and animal and plant products travelling from Britain to Northern Ireland are necessary to safeguard the Good Friday Agreement and peace and stability.
The European Union has renewed its legal action against the Bill since it was announced.
On Tuesday, French Europe minister Clement Beaune said there had been a “serene and confident” discussion between the 27 ministers in Luxembourg in response to “the recent provocative moves from the British government”.
“The protocol cannot be renegotiated,” he said.
But Mr Johnson said that the “reaction around the table amongst our friends has been much more muted than I think people were expecting”.
He added: “That’s because, you know, in the end, we don’t want to fall out over this. We want a solution.”
Mr Johnson also played down concerns about the legal challenges against the government over the Bill.
“We’ve got a legal case against us for failing to have proper customs procedures, all sorts of things,” he said.
Mr Johnson also rejected suggestions, from some leaders in the EU, that the attempt to redefine the protocol was to appease Tory hardliners.
“Do you really think that most Conservative MPs or most people in the country are thinking about this problem? They’re not,” he said.
“I’m afraid to say that this is an issue that is entirely to do with the balance of the political situation in Northern Ireland. And we have to respect that. This is something that I didn’t want to do. I wanted the protocol to work. I, after all, agreed the thing.”
The plans to unilaterally override parts of the protocol – agreed between the UK and the EU – have been working, according to Stormont Infrastructure Minister John O’Dowd.
He said he had come from a business event with more than 400 delegates and that people there said the dual access to the EU market and the British market is working for them.
Efforts to pass the controversial legislation must be stopped, Mr O’Dowd said as he appealed to MPs to vote against the bill.
Meanwhile, Unionists are against the imposition of checks between Britain and the north of Ireland.
The Democratic Unionist Party (DUP) refuses to return to the powersharing executive over the issue and has left Northern Ireland without a functioning government.
DUP leader Sir Jeffrey Donaldson said he hopes the bill gets through the Commons before Parliament’s summer recess.