Ms Foster, whose party propped up the current Conservative government, defended standing alongside Mr Johnson since he entered No 10 and said it was "right for the leadership of unionism in Northern Ireland to work with the prime minister of the day".
Asked if Mr Johnson's Brexit deal represented a "betrayal", she told the BBC's Today programme: "I think it says more about the person who broke their word, than me and leadership of the unionist party, the betrayal."
Mr Johnson admitted on Sunday that there would have to be some checks on goods travelling from Great Britain to Northern Ireland, if they were then destined for the Republic of Ireland.
But he continued to insist his Brexit deal will not create friction in trading across the Irish Sea, despite Labour's publication of an analysis - purportedly by the Treasury - showing that “at minimum” there would be at least some extra paperwork for exporters.
Ms Foster said customs officials had told her that there would indeed have to be checks under Mr Johnson's proposals.
Asked if she would be prepared to take the prime minister at his word in future, she said: “Well, once bitten, twice shy. We will certainly be looking for the detail of what this is going to look like.”
The DUP leader said that “free-flowing trade” between the different nations in the United Kingdom represented an integral concept of the union.
“If we are to have what has been proposed, then it wouldn’t be free-flowing trade, and that of course causes us great concern.”
Ms Foster said she agreed with Mr Johnson’s desire “to get Brexit done”, but added: “You cannot leave part of the UK in a worse-off position and leave us in a situation where we have checks between different parts of the UK.”
She said Mr Johnson had “moved away” from what he promised her at the Conservative Party conference, and said that “it is very important for us in Northern Ireland not just to have the word but to have the detail” in future.
Meanwhile, on Monday morning Mr Johnson began a final campaign push with a visit to a fish market in Grimsby, part of a tour of Labour heartlands that will also take him through the north-east and then south-west of England.
Mr Johnson was asked about reports that a four-year-old boy had to sleep on the floor while waiting for A&E treatment.
He told LBC: "Of course I sympathise very much and I apologise to everybody who has a bad experience.
"By and large, I think the NHS do an amazing job and I think that they deserve all praise for the service they provide - but they do need investment and that's why we're doing it now."