The Irish region, playing catch up to Pool One leaders Saracens, lead 26-3 after an hour thanks to a penalty try and a Conor Murray score but failed to make their dominance count, eventually running out 26-17 winners.
But highlighting Edinburgh's impressive displays in last year's competition, where they reached the semi-final stage, Penney was thankful his side mustered a healthy lead before the hosts' inevitable fightback.
Munster, who reached the quarter finals last year, must now beat Racing Metro at home in round six and hope other results go their way to ensure qualification and Penney admitted his side must raise their game next week.
"All in all, I've a pretty positive view of the whole situation," said Penney. "Given we had to come here and play at 12.30, it was always going to be a bit of a challenge.
"Edinburgh up here was always going to be a tough ask, even to just get the win. This time last year they were flying high in this competition and doing a great job.
"It was critical to get the win first. You could see when Edinburgh were able to unleash themselves in the latter part of the second half how dangerous they are, and if we hadn't got that buffer it was always going to be a problem.
"We got ourselves into a good, strong position and were able to be a bit more expansive on the back of that. It was just a wee bit disappointing we weren't able to capitalise on some opportunities which we created.
"We didn't score more tries because we weren't good enough fundamentally. Edinburgh just defended brilliantly. They just defended like their lives depended on it.
"We got the four points, we're in the fight next week and we'll see what happens on the back of that.
"Any team coming to Thomond is going to be in for a good challenging battle and I don't think it'll be any different next week.
"In fact, it should be a really exciting Sunday afternoon there with so much at stake on that one fixture."
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