The Clarets, who lost 1-0 to West Ham on Saturday, have won once in the last 15 league matches and have not scored since March 14.
Despite the seemingly bleak situation, Barnes is adamant Burnley will not give up hope and says they are determined to beat relegation rivals Hull this weekend.
“As a group of players we need to step up to the mark. It’s slipping out of our hands but we need to pull it back and win the next three now,” Barnes said.
“We’ll have to pick ourselves up for a massive game at Hull. It’s going to be a massive uphill battle but it’s one that we won’t give up on yet.
“We’ll have a good week in training and we’ll give it our all.”
Burnley’s defeat at Upton Park came after defender Michael Duff was sent off professional foul on Cheikhou Kouyate in the box after 23 minutes.
Mark Noble stepped up to score the resulting penalty to condemn Burnley to defeat and Barnes admits there is frustration amongst the squad that their performances have not been reflected in their results.
“We’ve shot ourselves in the foot again,” the Clarets forward admitted.
“Yes things have gone against us, of course, but you can’t just look at that, you’ve got to look at yourselves and take it from there.
“We should have won, it was a must-win game, we all knew that and I just feel dejection.”