The Independent called it a "shock ending" to Coleman's character, while The Daily Mail said it was "horrific".
Fans took to Twitter to complain about the "empty and useless" death, and the early viewing time of the episode that affected younger viewers.
Many said the scene left them in tears.
Showrunner Steven Moffat defended the scene to Sunday People, saying it was a scary sequence, but not harrowing.
"You have to be responsible about it - that doesn't mean it isn't shocking or troubling. But it is not like children learn about the realities of people dying from Doctor Who."
Coleman has appeared in three seasons of Doctor Who and admitted to Sunday People she was shocked by her character's death.
"It did not go in the direction I thought it was going to. But it's really cool and different, and good, I think. And sad ... I couldn't stop crying after I filmed my final scenes - it was ridiculous to get emotional. I'd planned all these things I wanted to say but only got two words out."
In New Zealand, Doctor Who screens on Prime TV on Sunday nights.
Capaldi is in Auckland for a fan event on Tuesday night.
- nzherald.co.nz