Missed payment on Amex - how screwed am I.

I didn’t realise that on my Amex it didn’t have automatic billing set up, a payment was to be done on the 20th March and I got a email on the 23rd March saying I had missed it and would be hit with a fee, I immediately paid the card and fee.

It’s already hit my credit file and across all 3 it’s plummeted by between 150 - 198 points depending on the credit report, I know this will stay on for 6 years. I feel embarrassed and stupid as I have never missed a payment before, but my concern is my fixed mortgage ends in 3 years and will this mean I’ll struggle to remortgage and if I do manage to remortgage is it likely I be given a higher interest rate?