Sunderland manager David Moyes said he wanted to steer Sunderland back into the Premier League as a 1-0 home defeat to Bournemouth, coupled with Hull's draw at Southampton, sealed their relegation fate.
Josh King struck for Bournemouth with time running out as Sunderland came forward in search of the winner, with the visitors having played much of the game's more positive football.
Sections of the home crowd called for Moyes to be dismissed, but he told the BBC: "I'd like to make sure we get Sunderland back in the Premier League.
"I think the plan when I sit down with the chairman is to look at how we can get the team back up.
"This is a great club and I feel for the supporters. We have to try and give them something to cheer about."
Moyes said he felt the defeat had "summed up our season," adding that he felt his side "played well for long parts."
"We had four or five good opportunities and did a good job," he added. "We're all disappointed and I feel more for the supporters. We take collective responsibility from top to bottom.
"We'll dust ourselves down and see what we have to do. We're disappointed with the level of performance all season, but we'll do everything we can to get it right."
Sunderland owner Ellis Short has admitted mistakes have been made during his tenure and said he had been left angry and disappointed by the club's relegation.
American businessman Short, whose continued backing is keeping a business with a net debt of £110.4 million afloat, promised to address the failings of recent years in a bid to reverse its fortunes on and off the pitch.
He said: "Like any supporter, my initial reaction is one of sadness, disappointment, anger and frustration. After 10 consecutive seasons as a top-flight club, the second longest in our 138-year history, it is hard for everyone to take.
"It is an especially cruel blow for our supporters, who have shown tremendous faith in the club. They backed the team, home and away, in huge numbers throughout the season and it is fair to say this season they have once again been relentless in their support. I am truly sorry that we have not been able to retain our top-flight status for them.
"I acknowledge that during my ownership mistakes have been made, particularly in the area of player recruitment, and as a result we have found ourselves struggling to survive in recent seasons.
"We had massive disruption during the summer transfer window and an unprecedented number of injuries throughout the season. These are difficulties which we have been unable to overcome and we are paying the price for that now.
"We need to improve, both on and off the field, and despite the bitter disappointment of today, there is a strong determination to do so throughout the club.
"There is significant work to be done over the summer and when the season is concluded, we intend to share our plans to move forward with our supporters."
Information from the Press Association was used in this report.
