Alan Pardew's side went down 2-1 to the 'Cherries' on Saturday despite being 1-0 up going into the last 13 minutes and Evans has admitted that the nature of the defeat was tough to take for several West Brom players.
However, despite a dismal run of form that has seen the club lose their last seven league games in a row, Evans is refusing to give up hope of avoiding the drop.
"I think there is hope," he insisted. "Even after the Bournemouth game there was real disappointment in the changing room. It's not like we have got to the point where we have accepted relegation.
"A lot of people have been writing us off. I understand with the position we are in it will be very difficult to get out of.
"There were a few tears after the game at the weekend because going into that game there was a lot of hope and optimism that we would get something from it and try to turn the season around even at this late stage. We were upset.
"We were ahead and then the game swung in the last 15 minutes and I think it has been the story of our season. It's hard to take sometimes.
"Mathematically, though, we still have hope and we keep going until it is mathematically not possible. We owe that to ourselves and the fans to do that. That's what we will continue to do that."
Evans was one of four players that were disciplined by the club after an incident during a training camp in Barcelona, but the Northern Irish international inssists that the incident had no affect on the club's form.
"I don't think it has reflected anything on the pitch," he explained. "People try and relate things that aren't always relatable but before we went to Barcelona and before the manager arranged the trip I think we were bottom of the league.
"Our performances throughout the season haven't been up to scratch. We haven't got enough points on board.
"It is very difficult. Sometimes it is important to keep your head and stay focused on your job on the pitch.
"We have quite a settled changing room and harmonious dressing room and we are all very friendly with each other. That has been a big positive for us. The place isn't completely crumbling like things have been reported on the outside."