Hughton was dismissed by the Canaries in April before Neil Adams was appointed interim boss.
However, four defeats from Adams's five games in charge saw the team relegated from the Premier League following three seasons in the top flight.
"Yeah, we got it wrong," Smith told BBC Sport. "It might have happened that if we got a caretaker manager in that we might have stayed up, but I would challenge anybody to sit round that table and do what we do and get it right.
"We didn't feel at that time there was anybody out there so we had a decision to make, do we bring in a kind of caretaker, so there were one or two names we were looking at, or go with a manager who is winning home games?"
Former Cardiff City boss Malky Mackay is the favourite to take charge at Carrow Road.