The world number one said: "I don't think it was the best performance, honestly, but in another way I can say I can play better, so that's a positive note from there.
"These kind of matches sometimes are more, brings better things for you in the future, because winning ugly always means that you overcome something that you weren't feeling great, you weren't feeling all your shots.
"I think [Hampton] surprised everybody a little bit today. I didn't really see her play before, but my coach watched and he said she didn't play like that other matches that he saw."
The American had been in a strong position in the third set, but a back injury allowed Azarenka to get back in to the match and ultimately take the win.