Britain's Home Secretary, Theresa May, ordered an in-depth review into Taser stun guns in October amid concerns they were being used too often against vulnerable people, particularly those with mental-health problems.
Ms Khan said it was the third incident where someone had died after being shot with a Taser since last year.
"This is a tragic incident and it's unclear whether he had a weapon. If he did not, he should not have been Tasered.
"This death supports what I've been saying - that Tasers can cause fatalities. It seems that excessive use of force by police is causing deaths."
She added: "I know there was a burglary, but does that mean that someone should lose their life?"
Man pleads 'help me'
Staffordshire Police said it was called to a break-in at a property in Newcastle-under-Lyme in the early hours of Monday morning.
The occupants of the flat, thought to be a couple in their 20s and their son, left before police arrived and a man remained in the property.
The man became unresponsive in a police vehicle and despite paramedics being called, he died.
The incident has been voluntarily referred to the Independent Police Complaints Commission (IPCC), the force said.
A neighbour, who declined to be identified, saw a "drunk-looking" man being escorted and supported by three police officers into a van.
He heard him call: "Help me" as he was walked along a path to the main road.
He said he heard shouting in the corridor and then banging. He became alarmed and he and his pregnant girlfriend left the flat.
Mark Finney, 50, who lives above the flat, said he heard tremendous banging, as if someone was in distress.
"Then I heard somebody shouting: 'Calm down, calm down."'
The shouting lasted for up to 45 minutes, he said. "When I got up this morning and heard the guy had been Tasered and had died, that's just shocking. It's upsetting."
In an IPCC report published in July, the Staffordshire force was shown to have the highest use of Tasers per capita in the country.
They were discharged on 72 occasions and drawn as a deterrent 547 times over nine years.
Tasers were only introduced in England and Wales in 2003 for use on people who presented a risk to police. Home Office figures show the use of Tasers has increased by 13 per cent in 12 months.
- Independent