Speaking on Tuesday morning the former Labour MP said the city would do what it could to operate as usual.
He said: "It is hard to believe what has happened here in the last few hours, and to put into words the shock, anger, and hurt that we feel today.
"These were children, young people and their families that those responsible chose to terrorise and kill.
"This was an evil act."
He offered his support to the families of the victims, and paid tribute to locals who had opened their doors to strangers and offered shelter to those fleeing the Manchester Arena and evacuated areas.
Mr Burnham said this was the "best possible message to those who seek to divide us", and would be the prevailing spirit of Manchester.
He said: "We are grieving today, but we are strong. Today it will be business as usual, as far as possible in our great city."
The former health secretary thanked the hundreds of emergency services personnel who worked through the night in the most "difficult circumstances imaginable", and those who had offered their support from other cities and countries.
More on the incident in Manchester: