Danny Graham has challenged his Swansea team to transform their "incredible" home form into away-day victories.
The dominant Swans defeated struggling Bolton 3-1 at the Liberty Stadium on Saturday and are just one of five Premier League teams unbeaten at home.
But 10th-placed Swansea are without a win on the road, their only away point coming in a 2-2 draw at Wolves.
"To be unbeaten in the Premier League at home after five games is incredible," said goal hero Graham.
"For a team that has just come up, I don't think that happens very often.
"But we need points on the road and that is what we'll be aiming to do at Liverpool."
Swansea's commanding triumph over 10-man Bolton was their third successive home win following victories over West Brom and Stoke.
And Brendan Rodgers' men, who have also drawn against Wigan and Sunderland at home, are alongside leaders Manchester City, Newcastle, Liverpool and Stoke City as the only teams in the top-flight with an unbeaten home record.
Only the top four and Arsenal have equal or better home records than Swansea - and Graham insists their home form gives Swansea belief ahead of Saturday's trip to fifth-placed Liverpool.
They have already travelled to three Premier League title contenders, losing at Manchester City, Arsenal and Chelsea, before the Welsh club were beaten at Carrow Road by fellow new arrivals Norwich City.
But Graham said: "We're starting to believe we deserve a place in the Premier League now.
"It takes a few games to get used to it and it was a sort of a reality check.
"But we're playing good teams and playing very good football against them and that will give us great confidence going into the Liverpool game.
"And we'll go there, give our best and try to pick up points."
Swansea have lost just three times at the Liberty Stadium under in Rodgers' managerial reign, fulfilling his ambition of making their home a "fortress."
But Swansea, who won Premier League promotion by winning the Championship play-offs last season, have won just seven times on the road during the manager's 15-month tenure.
"Home form is vital," said Rodgers.
"The players have big confidence at home and collectively we understand if we can do our job at home then we can control our destiny.
"We'll get better away from home as we grow into the season.
"It is fantastic for the supporters to go to a club with great history in world football but we're going to do our very, very best as the club has earned the right to play at these great clubs."
Swansea have never enjoyed a league victory at Liverpool and their 8-0 FA Cup third round replay hammering on their last visit to Anfield in January 1990 is the club's record defeat.
Graham, Scott Sinclair and Joe Allen scored as Swansea beat Bolton to prepare for back-to-back games with Liverpool and reigning champions Manchester United, who are the next visitors to Swansea.
Allen, who was not born when Swansea last travelled to Liverpool, admitted: "They will be two of the toughest games we'll play this season.
"But we are confident that we can go into those two games and still get something from them."