Adam Clayton says Boro are looking for a strong finish to the season to win back the fans' faith after relegation was confirmed on Monday night.
Boro bowed out of the top flight at the hand of a Chelsea side who are now just one win away from clinching the Premier League title but Clayton believes defeat at Stamford Bridge wasn't to blame for sending the Teessiders back to the second tier.
"It was a tough night," he said. "We've not got relegated playing against a team that are probably going to be champions, though.
"We've just got to go again and come back strong next year."
Five wins from 36 games has seen Boro slump to second bottom of the league table and Clayton says the team have rued missed chances across the course of the season.
"There are games that we feel we should've won and that's where we've let ourselves down when we could've gone for it and maybe didn't," he said.
"But as I say it wasn't tonight [against Chelsea], we got beat by a top class side.
"We sorry for the fans and we'll try and give them what we gave them last year and try to get back into the league."
Southampton arrive at the Riverside on Saturday for Boro's final home game of the season, before the campaign draws to a close with a trip to Anfield in two weeks' time.
Clayton says the onus must now be on finishing strongly and building early momentum ahead of next season's promotion push from the Championship.
"We've got to give the fans something to go off and give them some good performances to make them proud in the last two games," said Clayton.
"We'll try to get as many points as we can and go away with a bit of confidence knowing that we've got a team capable of coming back, challenging and coming to the party next time."