He also said the government would be "relentless" in chasing down the gangs who are facilitating the dangerous crossings.
The gangs appear to have begun loading more people into single boats in recent weeks, with the record 230 people arriving in the United Kingdom in one vessel in the early hours of Monday morning.
The inflatable boat was "buckling" in the water and could have led to a tragedy, French rescuers warned.
Asked about the 15 metre-long dinghy, the prime minister told GB News: "I know people will have been worried to see that image yesterday.
"It shows that the gangs are changing their tactics, but so will we – we will now change our tactics and we will be relentless in chasing them down.
"I said that when I visited Dover just over a week ago and I meant it.
"And I was there to change the conversation."
Burnham has said the government "will keep going at this issue" until small boat crossings are stopped but did not commit to a timeline.
He added: "I'd rather promise to people what I know I can do and what I know I can deliver, and that is a relentless focus on this issue to deal with the public concern."
Elsewhere in the interview, the prime minister suggested more affluent areas of the UK will have to house asylum seekers as well as poorer ones.
Burnham was asked about reports of a migrant camp being set up near Piddington, a village in Oxfordshire, which locals fear would overwhelm the hamlet.
He said: "It's obviously going to be challenging but I am prepared always to listen to people, to work with people and to pick up legitimate concerns, and I will address those concerns.
"I do have to say, we cannot have a situation where it's only the poorest communities in the country that receive all of the dispersal of refugees and asylum seekers. I do believe all parts of the country need to work, to play their part.
"We understand people's concerns and I will look into the issues raised by the good people of the Piddington."
