Eduardo Vargas thought he had earned QPR a point when his strike cancelled out Seamus Coleman's superb first-half opener at Loftus Road on Sunday.
However, Aaron Lennon's first Everton goal 13 minutes from time proved decisive for Roberto Martinez's men.
Defeat was harsh on the hosts who created plenty of chances and saw Junior Hoilett and Adel Taarabt both strike the crossbar.
"It is very disappointing to lose," QPR manager Ramsey told BBC Sport. "I'm hoping it can be showed how well the boys played and fought for the club.
"How we have not come away with three points is unbelievable."
A fifth straight league defeat - and a 10th in their past 11 games - leaves QPR four points adrift of safety.
However, with fellow strugglers Burnley and Sunderland both losing on Saturday, Ramsey is confident that eight matches is enough time to turn things around.
"Fortunately for us the other clubs around us haven't won and it keeps us within touching distance," he added. "We need to keep playing like that until the end of the season.
"I think we can get out of it, other teams have done that in the past.
"Had we gone out there with apathy and not played how we did then it would be different."
