Norwich's relegation was confirmed after defeat at Aston Villa.
But manager Smith insists his focus is on winning promotion next season - and has the backing of sporting director Stuart Webber.
"It's a bitter disappointment and I fully take my responsibility," he said. "There's been an inevitability about it and over the season our performances haven't been good enough.
"'I've got an English O-Level but I had to go and look at the word apathy this week after some debate from Norwich fans. We've tried hard.
"It's imperative we have a tilt at the Championship. The last two times our club has been in it, you've won it.
"We move on very quickly now and we are planning to get back up,' added Smith. We've got four games to go and the club is very well run. We've only got one player out of contract in the summer so there's not an awful lot we have to do.
"We've been planning for this for the last few months. We will move forward as a football club."