The Ukip leader also blasted British military interventions in Iraq and Libya as acts of madness which have helped radicalise people and acted as recruiting sergeants for groups such as Islamic State.
Nuttall was also critical of Theresa May over cuts to community policing, adding that Jeremy Corbyn “spoke a bit of sense” when he drew links to British foreign policy and terrorism.
Both May and Corbyn have put the response to Monday’s attack at the centre of the General Election campaign.
Ukip’s manifesto launch on Thursday, the first campaigning by a major party after the Manchester attack, also put tackling Islamic extremism at its heart.
Speaking to the Press Association as he met voters in Boston, Nuttall said: “I think our interventions in the past have helped radicalise people and have in many cases acted as a recruiting sergeant for these extreme organisations.
“But it doesn’t get away from the fact, or it should never be a way of condoning what has gone on.
“What this guy did is he targeted a concert made up of children and women and it just shows you how low these evil people will stoop.
“We’ve got to do more to cut this cancer out of our society.
“I’ve been accused of all sorts of things because I’ve described radical Islam or Islamic extremism as a cancer within our society, and frankly I’ll repeat it because it is a cancer and it needs to be cut out and it needs to be cut out as soon as possible, because if it isn’t then I fear that terrorist attacks like this will become commonplace.”
In a speech on Friday, Corbyn said the “war on terror is not working” and the deployment of troops on the streets following the Manchester attack was a “stark reminder” the approach was failing.
He said experts - “including professionals in our intelligence and security services” - had pointed to the connection between the UK’s involvement in foreign wars, such as the Libya intervention, and terrorism at home.
This led to criticism from May and other senior Conservatives that the Labour leader was trying to blame British military action for terrorist attacks.
Nuttall said: “As for what Jeremy Corbyn said yesterday, I think partly he spoke a bit of sense.
“I think our foreign policy since the turn of the century has been one act of madness after another.
“I think the war in Iraq was nonsensical and based obviously on bad intelligence.
“I think us going into Libya made no sense either, considering that we all pretty much knew that what was going to come after Gaddafi was going to be even worse.
“And if certain elements of the House of Commons had their way then we would be in Syria now and we would be bogged down in an even bigger war.”
Nuttall went on to say that community policing could play a “vital role” in tackling terrorism, with Ukip having pledged to recruit 20,000 extra officers in its manifesto.
“If a police officer is dug down into the local community and knows the people in the local community, people will feel far more confident in sharing information with that local police officer,” Nuttall said.
“So I think it is important that we review the number of police officers we have in this country and that’s why we’re absolutely correct in saying we want to see 20,000 more out on the streets.
“I think what Monday night proves is we’re living in different times now.”