QPR, in 19th place, have four games remaining to avoid the trapdoor to the Championship but travel to Anfield having not won there in the league since a 3-1 victory in 1991.
"We know it's going to be difficult but we're all up for it," Ramsey told a news conference on Thursday.
"The players were a bit deflated at the start of the week because they thought they had done enough to win the game against West Ham (a 0-0 draw).
"But as far as the mood has been, it has been quite good. We have got people like Joey Barton, Clint Hill and Richard Dunne going round and making sure our heads are not down.
"Nobody's chin is on the ground. We do believe we can stay up."
Ramsey is hoping QPR can take advantage of a fifth-placed Liverpool side that have dropped off the pace in the battle for Champions League qualification after a 1-0 defeat by Hull City on Tuesday.
"They are all must-win games for us now. We are four points away from our nearest rival above the line so we have to get as many points as we can now," Ramsey said.
"Liverpool have the quality and resilience to bounce back. They've been written off two or three times this season and Brendan's done a fantastic job in bringing them back to the levels that warrant a team of Liverpool's stature.
"But we believe we can beat anyone on our day and we're hoping that our day will be on the weekend."
(Reporting by Michael Hann; editing by Justin Palmer)
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