Relief was etched on Matt O'Connor's face after a storming finish from Bath and disciplined defending from Leinster allowed him just the faintest of smiles after falling over the line.

Relief at this stage of the season comes at the end of almost every game.

“You are always relieved when you win a knockout game,” said the Leinster coach.

“They had tremendous threat on the ball, Joseph, Eastmond, Banahan, Watson . . . I thought we did a good job for most of the game. We played in the right areas of the park, took our chances when they came and our scrum was outstanding.”

But Leinster were far from perfect and will have to correct a few areas before they face either Toulon or Wasps in the semi-final.

“We were a little bit inaccurate in the second half, missed a few kicks, fell off a few tackles,” conceded O’Connor. “Do that and you’ll have a difficult afternoon closing it out. I thought the decisions of Jamie (Heaslip) and the leadership group was outstanding and the kicking of Mads (Madigan) was tremendous today.”

The final penalty at the end of the match that went with Leinster and allowed Heaslip to kick the ball into the crowd proved to be pivotal. But there was no complaint from O’Connor given the three-point margin.

“There’s a load of 50-50 calls in the game. You can talk about a lot of incidents but I thought Jerome (Garces) refereed very well and he is as accurate as any of the referees in Europe at the minute.

Heaslip pointed to both the positive and negative aspects of the match but said that Leinster can now go into the next phase of the competition with their confidence high.

“They had a lot of pace in the back and very evasive runners,” said Heaslip. “If you switch off and make individual or system errors they will punish you and that happened twice. Do that and you make life hard for yourself as we did in the last 20 minutes.

“But we can take a lot of positives out of it and whether it’s Toulon or whoever in the next round, we can go into it with confidence. At this time of the season it’s just big game after big game. That was one of the fastest, toughest games we have played all season.”

The Bath team were uniformly not only disappointed with the three-point scoreline but with the team performance, especially in the first half, when they trailed 15-5.

Bath coach Mike Ford, however, believed his side could have won the game in the second 40 had a few decisions gone their way and had they not given away so much through indiscipline.

“A lot of disappointment, certainly the first half was better than that. I think that’s where we lost the game,” said Ford. "We didn’t control the ball and gave away too many penalties.

“They kicked their penalties. Fair play to them. But we’re very disappointed because we are better than that, especially in the first half. We couldn’t build any pressure with the ball in hand first half. We threw to ground, and of course the discipline side of it, and Madigan was pretty dead eye today.”

Ford also praised the Leinster defence, which held out the Premiership side in the last 15 minutes as they were chasing another score to draw level or overtake the home side.

“They have a decent defence don’t they," added the Bath coach. “They were always going to put us under pressure. Last 10-15 minutes I thought we were going to win the game . . . that last penalty. Small margins, small margins are going to win the game.

“We wanted to play quick and with tempo and they just picked us off. It’s the first time we’ve been there for a while but that’s not an excuse. We’ll watch the video and we’ll be even more gutted."

Bath captain Stuart Hooper reiterated his side's disappointment with the outcome but said that his team’s tactics were correct for Leinster.

“There’s a twofold disappointment,” said Hooper. “One is losing the game and individual mistakes in the first half. But our plan was right and I wouldn’t change it, but individually we let ourselves down in the first half.”

Bath outhalf George Ford said that he was trying to engineer a drop goal in the dying minutes but the Bath plays just didn't allow it, the penalty against them at the end calling time on their comeback

“At the end we could have held the ball a little bit smarter to try and get to 18-18,” said the downbeat English outhalf. “It was a three-point ball game at the end of the day and one or two better plays today could have done it.

"Yeah we let them back into the game. We kicked poorly and played into their hands. I'm delighted to get to the semi-final but disappointed about the last 15 minutes," said Leinster fullback Rob Kearney.

“That was a very, very quick game. The pace of it was savage. A lot of the guys were on their knees at the end. The pace of the semi-final won’t be much different. They were very good today. Even when the bench boys came on there was no difference.

“We’re in the business end of the season now and we’re in the unusual position in having to get back into the top four in the Pro12. That’s not ideal but that’s why you need a strong squad on big days.”