The Prime Minister is ultimately responsible, seeing as how she's nominally in charge of running the country. I don't see that she bears any personal responsibility but part of the job of any politician is to stand up and be accountable for what's gone wrong.
Sadiq Khan stood there and let himself be heckled, let the public vent their anger at him. Theresa May did not. Which approach is better? I wouldn't care to say, but it does seem like May is bad at engaging with people who disagree with her. Even when accepting accountability for the election shambles, she only did so when confronted by her own party -- ie, surrounded by friends, colleagues and allies. Not on election night itself, not on the doorstep of Number 10, and not since then either.
Also the interviewer was hounding her mostly over the question: "Have you misjudged the public's anger?" To which May's reply was "What the government has done is blablabla". That doesn't answer any aspect of the question at all, as it's neither about Theresa May personally nor about the public anger. Why shouldn't the interviewer interject, point out that she isn't addressing the question, and do so several times?