Conor Murray crossed in addition to a penalty try but the Irish side eventually came up short of the bonus-point win that would have improved their chances of reaching the knockout phase of the competition, but Penney was satisfied with the outcome.
"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," Penney said. "It was always going to be tough coming here. It was always going to be a tough ask just to get the win."
He went on: "You've got to remember that this time last year Edinburgh were flying high in this competition and doing a great job. They are a quality side and they've got a lot of pride.
"So, I'm really rapt that we got ourselves into a good strong position and we were able to be a bit more expansive on the back of that.
"It was a wee bit disappointing that we weren't able to capitalise on some of the opportunities which we created."
In the event, Munster left the Scottish capital with four points after the referee awarded them a penalty try and Conor Murray touched down, while Ronan O'Gara contributed the rest of the points with the boot.
"So, we got the four points, we're in the fight next week and we'll see what happens on the back of that," added Penney.
In the home camp, Michael Bradley was left ruing his side's luck, pointing in particular to the decision of referee Greig Garner to yellow-card captain Greig Laidlaw for a deliberate knock-on.
"We might have got a couple of calls last year. Going into the final day last year we had a negative points difference and we were getting calls like that. They've certainly got us back this year," said Edinburgh head coach Bradley.