Elliot was a substitute for the injured Tim Krul during the shock 3-0 reverse.
"Everyone is gutted, hugely disappointed, devastated - forgetting the three points, about what it means to everyone," he told nufc.co.uk following the final whistle.
"We have got to hold our hands up. We didn't do what we needed to do and we let ourselves and everyone else down.
"We have to look at ourselves and ask work out why we played like that after some good performances.
"This is the lowest point. You dream of playing in one of these derbies - I am so proud to play for Newcastle United - but then that happens, and it cannot happen again.
"It wasn't good enough, there are no excuses, and we have to make sure that this hurt drives us on now over the final five games. It feels awful and I never want to feel like this again."