Hull manager Steve Bruce admitted his side were "not good enough" after being relegated to the Championship.
City drew 0-0 with Manchester United but saw their chances of staying in the Premier League disappear after Newcastle's 2-0 win over West Ham.
"It's an awful experience and it will dawn on the players we are not in the Premier League anymore," said Bruce.
"There is talking and soul searching to be done. It is bitter and sad at the moment."
The Tigers - FA Cup finalists last season - were two points adrift of safety at the start of the day, needing a victory and for the Magpies not to beat West Ham.
But goals from Moussa Sissoko and Jonas Gutierrez at St James' Park took Hull's destiny out of their own hands, dropping down to the second tier after just two season.
They themselves could have beaten Louis van Gaal's side, but were not able to find a way past Spaniard Victor Valdes - making his full debut for United - who made two superb saves from Ahmed Elmohamady and Nikica Jelavic.
"In football, there are times when you feel like today; relegation from the Premier League. You are desperately disappointed with what has happened," added Bruce.
"Too many times I have come out and said we haven't done badly and not scored. The team in general have to create and score goals. We have had umpteen chances and not been able to take them.
"We all have to take the brunt of it, we have not been good enough. I thought at the start of the season we would have enough to stay in the Premier League but we have not done enough. You have to come back as strong as possible."
'I was not expecting this when I signed'
Defender Michael Dawson, who joined Hull at the start of the season from Tottenham, was in tears at the final whistle and said the Tigers should have performed better this season.
"Relegated from the Premier League, it is hard to take," said Englishman Dawson. "It was not today that relegated us, we had 38 chances to do it. Newcastle did the job and we didn't, we should not have been where we are.
"When I signed I was not expecting this. It is going to be a hard summer. We knew it was 0-0 for Newcastle at half time, and towards the end you get the feeling of the fans from their quietness."
|BBC Sport chief football writer Phil McNulty|
|Hull City's relegation is a devastating, shocking blow for The Tigers, manager Steve Bruce and owner Assem Allam, who has invested so much in the club.|
|Were they victims of complacency, of thinking they were safe with victories over Crystal Palace and Liverpool before slipping to defeat fatally against relegated Burnley at the KC Stadium?|
|Hull can reflect on that at length in the Championship and they must wait to see if 54-year-old Bruce will be leading that fight after signing a new three-year deal in March.|
|Bruce's transfer recruitment has been mixed, with buys such as Tom Ince and record £10m Uruguayan striker Abel Hernandez failing miserably.|
|Now they must rebuild from the Championship - but how many of this squad will be around to revive a club that reached the FA Cup Final and survived in the Premier League only a year ago?|