The Cottagers are 13 points from safety with eight games remaining in the season.
Speaking before this weekend's clash with Liverpool, Parker said: "I believe we can stay up, in this league I see the quality in this team but I know and understand it will be very difficult. When you look at how many games we need to win I understand it will be very difficult. While there's still points it's possible.
"There's only so many more weeks I can go on saying i believe, but while there are points there's still that hope. One result can kick start something and we have the quality to try and do that.
"People can fire back we've had long enough, but i still have that belief.
"We have some very good footballers and we need to start getting the best out of them. The attitudes and standards are rising on a daily basis. They have a chance, at the weekend, to prove how good they are."