Adam Clayton says Boro must show the endeavour and fight displayed against Arsenal in the season's run-in.
Goals from Gunners duo Alexis Sanchez and Mesut Ozil, either side of Alvaro Negredo's strike, undid plucky Boro on the night.
But Clayton says Boro must carry the positives into the six remaining Premier League fixtures.
"No-one can accuse us of not giving it a go," the midfielder said.
"We were fast and strong in the tackle, and we were on top for large periods.
"We've left everything out on the pitch and I think we deserved to get something from the game.
"Now we've just got to attack these last couple of games and keep that spirit."
Clayton says it's down to the players to ensure Boro are on the right side of fine margins in coming weeks.
"No-one's blown us away this season, we've competed with every team," he said.
"But maybe that's been the story of the season a little bit - we've given everything but not been able to put the points on the board.
"That's down to us, we need to win a few of those narrow 1-0 or 2-1 games. Three points changes everything.
"We'll keep going until we can't do otherwise, we've got to go to Bournemouth and give our all like we did [on Monday].
"We still believe we can turn it around."
Clayton also praised the Boro fans for backing their side to the hilt.
"These fans are the best I've played for," he said.
"It was a great atmosphere and game to play in under the lights at the Riverside.
"They keep you going when you are 1-0 down and keep digging in. When we got the goal, the place was rocking.
"We want to reward them with a win - that's our main aim.
"We won't be giving up. There's more than enough points to play for and we'll go again."
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