Morrell’s men were 4-0 down after just half an hour and even though they scored a consolation goal in the second half, the Lambs were soundly beaten.
It was another disappointing performance after last Saturday’s 3-0 home defeat to Leamington and Tamworth are now four points adrift of the top seven.
Something must change for the Lambs and Morrell concedes it might be him if results don’t improve.
The ex-Wrexham chief told the Birmingham Mail “I thought I was embarrassed against Leamington but that first-half showing against Nuneaton was by far the worst I have ever had as a manager.
“There was no effort, no cohesiveness, no real desire in a derby game to go and win a ball.
“They chucked the towel in after ten minutes and that is unacceptable. There are going to have to be big changes and if I’m not careful it might be me. Things can’t go on like this performance.
“It hurts me, of course, it’s not good at all. But I am going to be coming out swinging. Our backs are against the wall and so we have got to, there’s no other way.”
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