Following defeats at Ospreys and Stade Francais, Edinburgh bounced back to win against Ulster and Munster - thanks to improvements at the breakdown area and increased levels of physicality.
Now head coach Moffat acknowledges that same level of progress needs to continue against a Dragons side that Edinburgh have only beaten once in the past two years.
Moffat said: "The Dragons are a tough nut to crack. They are a very physical side, but they play some good rugby as well.
"The main challenge for our team is maintaining consistency levels in key areas of our game. That is what we will be looking to do again this week and not allowing our performance to drop off.
"We know we didn't perform well against Ospreys and Stade Francais. We were up against two good sides away from home, but we didn't perform to the levels we expected.
"The positive aspect to come from those results is that we have addressed some important areas of our game.
"During our last two wins, physically we have been good and our work at the breakdown has been good.
"We are aiming to continue that this week and hopefully play some more rugby as well."
Moffat revealed he has delayed announcing his final starting line-up with a couple of members of the first team squad carrying knocks from last Friday's victory.
Wing Mark Robertson and utility forward Fraser McKenzie, who can play either at lock or blindside flanker, have been added to the 22 which defeated Munster.
But Jim Thompson (knee) and Simon Webster (Achilles) are still on their way back to full fitness and are expected to play for Gael Force, Scottish Rugby's British and Irish Cup team, at Doncaster Knights on Monday (2 November).
Club captain Simon Cross is still recovering from a serious knee injury and joins long term absentees, Ross Rennie (knee) and David Callam (hip) in the treatment room.
Meanwhile, Scotland lock Jim Hamilton (knee) is still receiving treatment and expected to be a handful of weeks away from resuming competitive duties.
Edinburgh squad for the Magners League match against Newport Gwent Dragons at Murrayfield (Sunday, 1 November, kick off 5.05pm, live on S4C): (Forwards) Allan Jacobsen, Kyle Traynor, Ross Ford, Andrew Kelly, Geoff Cross, Scott MacLeod, Craig Hamilton, Steve Turnbull, Alan MacDonald, Fraser McKenzie, Roddy Grant, Allister Hogg, Scott Newlands. (Backs) Mike Blair, Greig Laidlaw, Phil Godman, Tim Visser, Ben Cairns, Nick De Luca, John Houston, Andrew Turnbull, Steve Jones, Mark Robertson, Chris Paterson.
Supporters are reminded that this Sunday is 'Fancy Dress for Dragons' at Murrayfield where the fan with the best Halloween costume will win a prize (two tickets to the Scotland v Fiji, Bank of Scotland Corporate Autumn Test match).
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