Last weekend's defeat at Manchester United was their 10th in 11 away fixtures and also stretched their run to 10 league games without a win.
The 3-0 scoreline was a disappointing one for Laws in his first match since being appointed Clarets manager, but the team's performance - which saw them hold the champions for more than an hour and create some opportunities of their own - gave him plenty to be encouraged about.
It came on the back of the third-round victory at MK Dons which set up Saturday's tie at the Madejski Stadium, and Laws is hoping that another morale-boosting away win will give his new charges further belief that they can cure their travel sickness in the league and start to pull themselves up the table again.
"It's a record that we are not proud of and it's something that we have to overcome," Laws said.
"Every game that we do win away from home is a benefit to us as it grows the confidence.
"They went to MK Dons and got a result and will benefit from that as much as if we get a result against Reading.
"It will be exactly the same and it leads you into your next Premier League game on Tuesday against Bolton with the confidence of knowing that you're a bit more organised and harder to beat. It will be very encouraging."
Burnley reached the fifth round of the FA Cup and the Carling Cup semi-finals last year, as well as mounting a successful promotion campaign in the Coca-Cola Championship.
Those achievements defied the widely-held theory that a cup run can disrupt a team's progress in the league, and Laws believes it will only be to Burnley's overall advantage if they make it through to round five again.
"Everybody was thinking Burnley would wear out last season because of the amount of games they were playing in cup competitions and keeping an eye on the league with not the biggest squad," Laws said.
"But that just shows you the character within the squad that they could cope and that they were enjoying every minute of it.
"I have no problem with that, and I think putting our strongest team out against Reading is important because we want to try to get a settled side as quick as we possibly can. A settled side will be a more organised side."
Laws has been looking to strengthen his squad and is confident of tying up a deal for French forward Frederic Nimani in the next 24 hours.
The Clarets are in talks with Monaco about taking the 21-year-old on loan until the end of the season.
"He is a player that we are talking to and we are hoping to try to do something over the next 24 hours," Laws said.
"We've had talks with them (Monaco) and he's trained with us.
"The thing that is important is to get things right first before we start saying we have got this player or that player. But we are tapping into a lot of players and he's one of them.
"We are very confident that things can be worked out, but until everything is signed and sealed, that's as much as I can give."