Albion suffered a crushing 2-1 defeat to the Cherries last weekend, having conceded twice in the final 13 minutes after Evans was forced off because of illness and injury, to leave Alan Pardew's side 10 points adrift of safety with only seven games remaining.
The Baggies have now lost seven successive Premier League games and have won just once in the top flight since August, yet Evans maintains the squad have not accepted their fate is already sealed.
"I think there is hope," said the center-back, who spoke at the launch of a collaborative project between the Irish Football Association, Ulster GAA and Ulster Rugby called Sport Uniting Communities.
"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."