With Welsh rivals Scarlets also winning, it saw the club drop down to seventh in the table, with Cardiff Blues the only other Welsh side below them.
They do however get a chance to close the gap on both Scarlets and fourth-placed Ospreys this Friday when they travel to face reigning RaboDirect PRO12 champions Leinster.
And with all the focus now on the league following their exit from the European Challenge Cup and LV= Cup last month, head coach Edwards backed his side to be in the mix as one of the best placed Welsh sides.
"We were very under-prepared going into Edinburgh because of the weather conditions but now we've had a good training week so we're better prepared and fresh," Edwards told the South Wales Argus.
"It's good to have a break sometimes. This league is pretty relentless for Welsh teams and we didn't get a break whereas the Irish teams had a few weeks off.
"We've got that game in hand now on the Scarlets and if we'd have won last weekend we would have been standing second in the ranking of the Welsh regions.
"And if we manage to do that this season that would be a magnificent achievement.
"There would be a little mini-battle between the Welsh regions in the league and that would be exciting.
"We want to finish as high as possible and these matches over the next three weeks are really key to that."
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