Edinburgh led with 10 minutes left but prop Pierre Schoeman was penalised for barging Tadhg Beirne with his team in control of the ball, and Keith Earls dived over in the corner soon after Munster kicked the penalty into touch.
Earls had scored the first try of the contest with Beirne in the sin bin after Edinburgh had failed to make the most of three penalties inside the 22.
Chris Dean’s try and Jaco Van Der Walt’s kicking put the hosts in the driving seat in front of 36,358 fans at BT Murrayfield, but the visitors comfortably saw out the win after a brilliant and crucial conversion from Tyler Bleyendaal.
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Cockerill said: “It was one hell of a contest and tiny, tiny margins decide these things – a penalty that gets reversed, a line-out that’s overthrown that bounces their way and in the ensuing play they score.
“But we had opportunities to score in the first half which we didn’t take, we had massive moments defending our own line.
“Even from our first try, I thought their player knocked it on. It’s tiny margins from the officiating.
“It was two very good teams going very hard at the game. I’m very proud of how we performed. Munster are a great team and we are now able to compete at that level. We have got to learn how to win these tight battles. In the tightest of moments they have got to be better.”
Edinburgh players complained Henry Pyrgos had been slammed to the ground just as Earls took a quick penalty to dart over to open the scoring, but Cockerill would offer no opinion on the controversy without another look.
But he added: “It’s the differences from a referee, the bounce of the ball, a bit of discipline from Pierre Schoeman at the end and you’re kicking a goal and you are six points up and win the game.
Quality from Keith Earls! ?
Quick thinking and quick feet gives Munster the opening score of the Champions Cup quarter-finals ?
Intelligence = ? pic.twitter.com/A1y2mmewpd
— Rugby on BT Sport (@btsportrugby) March 30, 2019
“That’s life, I am not going to criticise Pierre because he’s a committed player and he does what he does and I’ll back him to the hilt. But those are the falls sometimes.”
Munster secured their 14th victory from 18 Champions Cup quarter-finals and head coach Johann Van Graan attributed their winning mentality to the people who make up the club on and off the park.
“If you were inside the bus when we arrived here, it was breathtaking to see the supporters,” he said. “It felt like we were going to play at home.
“And in terms of the group, that’s why I came to Munster, because of what Munster is about. It’s about passion, integrity, real heart and real grit. Munster never seem to do it the easy way and we certainly didn’t do that today.
“I am incredibly proud to be the coach of this team.
“It’s our third semi-final in a row and this was a big win for us. Just look at the history of European rugby, you don’t come away with away quarter-final wins.”
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