They are still alive in the competition. A bonus-point win over Racing Metro in Limerick next Sunday will see them finish the pool on 20 points.
But where those tries might come from is the question that will surely haunt Rob Penney's thoughts for the week.
The worry from Munster's perspective was that when a side is as woefully inept as Edinburgh, you run the risk of being dragged down to their level. With tries at a premium, it was a gamble, and one that ultimately backfired as Munster scored just half the requirement over 80 minutes of poor fare.
Munster were lethargic, showed little or no innovation – except for the increasingly impressive Simon Zebo – and finished the game with the look of a side that is bereft of confidence.
The confusion and debate over game plans is clearly beginning to take its toll on the players, many of whom looked stale yesterday.
It defied belief that five times in the first half O'Gara took aim at the posts.
The kicks were well with his range, but ignoring the touchline was obviously a struggle for him. A previous incarnation would have kicked for the corner and trusted his forwards to win the subsequent line-out and maul over for a try.
At least twice he sought to change Doug Howlett's mind over the decision to take the easy three points. The captain was not for turning though, perhaps influenced by the butchered line-out early in the game when a chance to attack the Edinburgh line was wasted with an over-thrown dart.
It was crucial, Penney said afterwards, that O'Gara did keep the scoreboard ticking over during the first half with the emphasis on securing the four points – "our priority was to win the game," said Penney – but the coach must be silently seething at the opportunities wasted over the 80 minutes.
When Dave Kilcoyne picked and went just before half-time, for example, the prop was obviously going to be stretched to reach the try-line when he went to ground, but instead of being patient and recycling the ball, he went for it and knocked on.
Similarly, twice in that half Munster had an overlap when on the attack but on both occasions Felix Jones failed to look over his shoulder and died with the ball.
It is on those split-second decisions that tougher games than this are won and lost.
Perhaps that is why prominence was put on winning the game and not chasing the bonus point.
In a way it is hard to argue with Munster's pragmatic approach, especially when remembering that when they eventually ran a penalty close to half-time, a combination of a poor pass from O'Gara and poor handling by James Downey saw the try-scoring chance wasted.
It will, however, be hugely frustrating for Munster when they review the tape and realise just how many tries and points they left behind them. They routinely savaged the Edinburgh scrum and on the rare times they mauled the ball they made huge gains.
Indeed, so in control were they at scrum-time that their penalty-try award came during Kilcoyne's spell in the sin bin (48-58), ironically just moments after a despairing Munster supporter gave voice to his frustrations with a "four penalty tries, we need four penalty tries" chant that momentarily lifted the gloom that had descended on the near-empty Murrayfield.
The penalty try was followed up by some of Munster's most encouraging play as they continually battered their way over the gainline with a succession of pick-and-go moves.
Peter O'Mahony was impressive at this stage, and Edinburgh were there for the slaughter.
When Conor Murray challenged around the fringes and touched down with just over an hour gone, the hope was that Munster would kick on and secure the two more tries.
By now there was no question that Munster were the better team.
They enjoyed lots of possession and were repeatedly presented the ball by an Edinburgh team that was devoid of innovation. When the killer blows failed to come, however, Edinburgh grew in confidence and, buoyed by Munster's self-doubt, they began to wear down the visitors.
Douglas Fife capitalised on a Grand Canyon-sized gap in the defence when he charged through to touch down late on, and then five minutes later the defence was again embarrassed when the winger came through to reduce the gap at the end to nine points.
That Munster were made to look so ordinary in defence at a time when they should have been lording it is the great imponderable.
How could they allow themselves to be dragged down to Edinburgh's level?
What exactly is Munster's level is a far more awkward question, and one that will surely have caused Penney another sleepless night.
For now the coach will be focusing on what he can control and what is needed next weekend.
It is straightforward enough, with four tries and a bonus point required. Where those tries are going to come from is another awkward question.
EDINBURGH – G Tonks; D Fife, B Cairns (B Atiga 55), M Scott, T Visser; G Laidlaw, R Rees; R Hislop (A Allan 70), S Lawrie (A Titterell 49), W Nel (G Cross 70); G Gilchrist (N Talei 70), S Cox; S McInally, D Basilaia (R Grant, h-t), D Denton.
MUNSTER – F Jones; D Howlett, K Earls, J Downey (C Laulala 63), S Zebo; R O'Gara (I Keatley 65), C Murray (D Williams 70); D Kilcoyne, D Varley, BJ Botha; D O'Callaghan (B Holland 70), D Ryan, P O'Mahony, T O'Donnell, J Coughlan (W du Preez 50-58) (P Butler 65).
Ref – G Garner (RFU)