How do I take phone calls without the caller thinking I'm dumb?

How do I take phone calls without the caller thinking I'm dumb? I had a phone screening interview for a job on Monday, but the caller was about to hang because she said I was unprepared. I made up an excuse said that my phone signal was weak and we continued. I sent an email later to inform her of my stutter because I didn't mention it during our call. Does a stutter make you sound unprepared and what I can do to avoid this again?