The home defeat was their worst result since 2016.
It leaves them in the bottom three on 21 points, a point behind Watford and West Ham, with a worse goal difference than both.
"Two of the sides below us were playing each other and with us against Man City, you didn't need to be a betting expert to see we would be in the bottom three today," said Smith.
Danny Drinkwater, who has only played three games in 17 months, was at fault for City's first two goals and looked off the pace as Villa struggled.
"Danny will make us a better team," said Smith. "He has looked good in training and he got 75 minutes today, which he needed. He was not the reason we lost 6-1."