Norwich were relegated from the Premier League on Saturday after a 2-0 loss at Aston Villa.
Burnley's dramatic late comeback from 1-0 down to beat Watford 2-1 left the Canaries 13 points adrift of safety with just four games remaining.
It was an unhappy return to Villa Park for Norwich boss Dean Smith as goals either side of half-time from two players he signed for Villa, Ollie Watkins and Danny Ings, earned Steven Gerrard's men the three points.
Smith has been unable to turn around a sinking ship since replacing Daniel Farke in November.
"I'm disappointed for a lot of people -- the owners, the supporters and everyone to do with the football club," Smith told reporters.
"I take part of the responsibility because I've come in here to try to keep us up and unfortunately we haven't done enough, but that isn't down to the performance today (Saturday).
"Unfortunately, in a lot of the bigger games this season, we've not quite reached the levels that we need to," he added.
The Canaries have gone down in each of their last three campaigns in the English top-flight, having also been relegated in 2015/16 and 2018/19.
"Ultimately, we haven’t been good enough and the quality of our squad to stay in the Premier League hasn’t been good enough, so we'll learn from it," said Smith.
"We have to come back stronger for the last four games and then next season."
Norwich captain Grant Hanley told the BBC: "I'm disappointed with our result. It is probably fair, we haven't been good enough this season.
"It is difficult for me to comment on anything right now. Emotions are high, we gave our all but it wasn't enough and (it was) the story of our season."
Watford's 11th consecutive home loss also leaves the Hornets on the verge of relegation.
Everton's 68-year stay in the top flight is now in severe peril as the Toffees are five points off safety, but do have games in hand over Burnley and Leeds to come.