David Moyes felt Sunderland deserved something against Middlesbrough but vowed to keep fighting to escape Premier League relegation.
Marten de Roon's eighth-minute strike consigned bottom side Sunderland to a 1-0 defeat against their fellow strugglers at the Riverside on Wednesday.
Didier Ndong and Wahbi Khazri forced Brad Guzan into saves with shots from outside the box, but the Boro keeper was largely untroubled across the 90 minutes.
Sunderland now sit 12 points adrift of safety at the foot of the table, and the Black Cats will be relegated this weekend if Hull City avoid defeat at Southampton and they fail to match their result against on Bournemouth on Saturday.
Moyes rued a missed opportunity to move closer to safety but is refusing to throw in the towel.
"We started great and actually we played well throughout the game tonight, but we gave away a poor goal," he told Sky Sports.
All over at the Riverside Stadium pic.twitter.com/udBVF2SE1a-- Sunderland AFC (@SunderlandAFC) April 26, 2017
"We certainly deserved to get something out of the game. We only gave up two opportunities in the whole game. We had some that weren't clear enough, but it wasn't for the want of trying from the players.
"We will continue fighting. We know the position isn't good and every game that goes past makes it harder.
"I felt tonight this is one we had to win, but we'll get another chance to win on Saturday so let's hope we can put in a similar performance which leads to goals and hopefully three points."
Head coach Steve Agnew got his first taste of victory since taking over from Aitor Karanka, ending a 16-match winless run in the Premier League in the process.
While Boro are now just six points adrift of safety, they face Manchester City, Chelsea and Liverpool in their remaining four matches.
Agnew insists they will approach each match as it comes, though he acknowledged the magnitude of Sunday's encounter with City at the Riverside.
"We were looking for a reaction after the disappointment of Saturday and no better way to get it than against our north-east rivals," he told Sky Sports.
"Second half we did defend a little deeper than I would've liked, but you saw the fighting spirit and determination. Sometimes if you show qualities like that then obviously it's a different way of winning.
"There's three points and it closes the gap again. We just prepare now for a massive game on Sunday.
"That's why we're in the Premier League, to compete against the biggest teams. We have Manchester City coming up and that's a game we look forward to."