Nathan Redmond inspired a 4-2 win over Watford at Carrow Road, but it was too little, too late for the Canaries, who returned to the Championship 12 months after coming up through the play-offs.
Sunderland’s victory over Everton rendered Norwich’s ninth win of the season – and third in 17 games – irrelevant as Neil’s side joined Newcastle and Aston Villa in being demoted.
“My future doesn’t really concern me at this moment in time,” Neil said.
“I’m really disappointed and gutted that the club’s gone back down to the Championship and that we didn’t manage, under my management, this season to keep the club in the Premier League.
“A lot has happened in the last week. At this moment I’m just trying to come to terms with what’s happened on the pitch and where we find ourselves.
“I want to sit down with the owners (Delia Smith and Michael Wynn Jones) and have a good chat with them.
“There’s a lot of soul searching and discussions to be had to decide which way the club is going to move forwards.”
David McNally resigned as chief executive after last Saturday’s loss to Manchester United, but chairman Ed Balls publicly declared Norwich’s backing for Neil on Tuesday.
And home fans sang in support of Neil in the second half and during a lap of appreciation following the final home game of the season.
The Scot, appointed in January 2015, added: “That, for me, was really, really humbling.
“I feel as if I’ve let them down. I feel as if we’ve come up short as a group, as a club.
“For them to respond in that way, I didn’t expect. I think it’s really unusual. I can only thank them for that.
“It makes it even more difficult for me to accept that we’ve come up short.”
The Canaries ended a four-match scoreless run with goals from Redmond, Dieumerci Mbokani – who scored twice – and a Craig Cathcart own goal.
Since a 3-2 defeat of Newcastle on April 2, Norwich had lost four straight games, including 3-0 at home to Sunderland.
Neil rued the fact his side performed when it was too late.
“It would’ve been a better performance if it had been against Sunderland when it mattered,” he added.
“The Sunderland game was a game where we had it in our own hands and we could’ve put it to bed really and we didn’t.
“It’s always tough to pinpoint one or two games, I think there’s a whole host of games over the course of the season where we’ll look and think we deserved a bit more. Ultimately you’ve got to do enough.”