I've only been put under once and it was when I was very, very young (3 for hernia surgery, I'm in my mid-40s now) and I had a similar experience, except I came to ~half way through and picked up my head, wondering what the fuck was happening to me, before promptly being put under again. It's my earliest memory but it's also one of the only strong memories I have before 6-7 years old.