Lock Carlo Antonio del Fava was then sent to the sin-bin and Moffat's men took advantage with Allan Jacobsen crashing over for a try and Scotland hopeful David Blair, who had earlier missed a crucial kick, landing the conversion.
That proved enough to secure Edinburgh's second win on the trot after a woeful start, following the 32-24 success over Leinster, but Moffat is demanding more.
"I know the conditions were a bit greasy with the dew on the ground, but that was no excuse for our performance," said Moffat.
"We are a lot better than that and I want us to show it but at least we have won the game, which is the most important thing.
"At the end of it all, though, a win's a win. You take them however they come and this, I have to admit, came from a really scrappy game.
"David did really well at the end for us - it can't have been easy for him, after that earlier miss."