Reading's reward is a home draw against Burnley, and with the Clarets having lost 10 out of 11 away fixtures in the Barclays Premier League this season and currently only a point away from the relegation zone, another upset could be on the cards.
However, Burnley are no strangers to cup success themselves, having reached the FA Cup fifth round and the Carling Cup semi-finals last year when they were a Championship side.
The squad boasts an impressive pedigree and despite Reading's exploits in the previous round, Laws is not expecting to see the underdogs win through again at the Madejski Stadium.
"I am delighted for them (Reading) because it keeps their cup run going and I know they are struggling financially," said Laws, who was a spectator at Anfield last week.
"This will be a great relief for them and they will be looking at us and maybe looking at our away record and thinking there's another opportunity to progress in the FA Cup.
"But I think Burnley have already shown last season that they have an appetite for the cup competitions.
"It never affected their league performances, so lets hope we have the same again - that we have a good performance away, a good cup run and that that kicks us on for the league."
Laws only took over from Owen Coyle at Turf Moor last week, but with a sequence of crucial fixtures on the horizon - including a trip to Coyle's Bolton next Tuesday - the new Burnley manager has had to act quickly to put the wheels of his regime into motion.
The assembly of the club's new backroom staff has been completed over the last few days and with a full week of training now under his belt, Laws is pleased with the way things are progressing.
"It's about settling in as quickly as you can," Laws said.
"The players want organisation and direction and that's something we are trying to put in place immediately.
"Obviously with not having had a lot of staff around it has been more of a strain, but now we have got everything in place, it's about motoring forward and hitting the ground running, and the players over the last few days have been excellent.
"They have been attentive and understood that we have some work to do and the planning for the FA Cup and the league games is now well under way."
Laws has been boosted this week by the return to fitness of Jay Rodriguez, Chris McCann and Martin Paterson, all of whom have been sidelined with injuries since September.
The trio made their comebacks in a reserve game on Tuesday and should all be available for selection against Reading.
Steven Fletcher had to come off with a knock to his ankle in last week's defeat at Manchester United but should feature and Clarke Carlisle has returned to training after overcoming a side strain.
Club captain Steven Caldwell will miss out again though after suffering a setback in his recovery from a groin problem, while David Nugent is ineligible for FA Cup matches under the terms of his current loan deal from Portsmouth.
Andre Bikey is still with Cameroon at the African Nations Cup.