The Canaries fell to a 2-0 defeat against Aston Villa as their hopes of Premier League survival officially came to an end.
Dean Smith took over the managerial position from Daniel Farke halfway through the season, but failed to turn around the club's fortunes.
Speaking after the defeat, the manager said: "Obviously I'm bitterly disappointed and I fully take my responsibility as well.
"I think over the last four to five weeks there's probably been an inevitability about it.
"I'm disappointed that we got relegated today because I thought our performance was good, but unfortunately over the season, the performances have not been good enough and we've lacked the quality required in this league…
"(The players) are very down, very dejected. I won't know my own feeling on getting relegated until I've felt it over a few weeks but we have to reflect and move on very quickly now to planning to get back up."
Norwich have lost three games on the trot and are currently bottom of the Premier League with just 21 points to their name.
The Canaries had the same number of points when they were last relegated back in the 2019/20 season.
Norwich will now be looking to return to the top tier at the first time of asking for a second time, with Smith adding: "I've got an English 'O' level but I've had to go and look up the word apathy because there's a lot of talk about that between our supporters and the football club and I don't see that at all.
"We're a one-club city and it's imperative we stick together and learn our lessons and get ready for another tilt at in the Championship.
"The last two times we've been in the division we've won it and that's what we look to now."
Norwich return to action next weekend when they host West Ham at Carrow Road.