Burnham cited the 2016 EU referendum and the 2014 vote on Scottish independence.
“What we find is that the risks that come from those situations take a long time to heal and it sets you right back, and you can’t focus on what’s right in front of us here and now,” he added.
“The cost-of-living pressures that are hurting people in Northern Ireland, the need to get that budget set so that public services can function as they should.”
He continued: “A decade since the Brexit referendum I think we’ve had too much division, too much arguing, too much backward-looking.
“We need to fix the things right in the here and now.”
Burnham said that people in Northern Ireland “want more breathing space from the cost of living, good, well-paid jobs and opportunities for their children”.
“Political point scoring in the past has made this harder, not easier,” he said in a statement ahead of his trip.
“We need to be better, so I want to work with the Northern Ireland Executive and the main political parties to try and make a real difference to communities here, and that’s the message I’ll be taking into my meetings later.”
Before meeting the politicians, the prime minister heard from young people about the issues that impact their lives and their aspirations for the future.
He spoke to teenagers and staff involved in mentoring schemes within Belfast’s creative music scene – which seeks to elevate local artists and promote the city as a UNESCO City of Music.
Earlier on Thursday, Burnham travelled to south Wales – his first official visit to the country since he became prime minister.
Before the trip Burnham announced plans to bring together the leaders of Wales, Scotland and Northern Ireland in the autumn for a summit to help boost the UK economy.