Leicester attack coach Peter Hewat tells Premier Sports: "Very disappointed. We defended well in the first half, took a lot of pressure and made a lot of tackles.

"We gave them easy entry into our 22 in both halves and by the end that took its toll.

"Our mentality was pretty good. We just probably weren't accurate and let ourselves down a little bit.

"Every game now feels like a knockout game and that's the way we're treating the next one. We'll have a few days off and then get back into it."

Glasgow Warriors head coach Franco Smith tells Premier Sports: "I still feel we made a lot of errors, a lot of mistakes, which is down to nerves. Some tries left out there but I'm happy with the result.

"We're getting better as a group and we didn't want to disappoint.

"Leinster pose a completely different challenge. They know how to handle strategic moments in the game. They've got the complete package, a good rush defence - they put you under pressure.

"It's going to be difficult with guys coming back in the next few weeks. We'll see how we approach this week. The boys out there tonight played well, but one or two fresh players might add value."

Image source, SNS

Tom English
BBC Scotland's chief sports writer

Glasgow have waited for so long to win a knockout game in Europe’s top-tier competition. They did it very comfortably tonight.

Still missing Tuipulotu, Jones, Dempsey, Cummings, Williamson but they were dominant.

Dublin next. They’ll be underdogs, yes, but they possess a helluva bite.

Six tickets are booked for the quarter-finals, two places remain. Who will complete the line-up for the last eight?

Quarter-final draw (ties to be played on the weekend 11/12/13 April):

• Bordeaux-Begles or Ulster v Munster
• Toulon v Toulouse or Sale Sharks
• Leinster v Glasgow Warriors
• Northampton Saints v Castres

Semi-final draw (ties to be played on the weekend 2/3/4 May):

• Bordeaux/Ulster/Munster v Toulon/Toulouse/Sale
• Leinster/Glasgow v Northampton/Castres

Fraser Brown
Former Scotland hooker on BBC Radio 5 Sports Extra

Probably the perfect night for Glasgow and Franco Smith.

Great performance. In the first half, they didn't put the points on the board that they should have. The 10-minute blitz at the start of the second half was all they needed.

It allowed them to rotate, bring the subs up nice and early, and wrap the players up for what is going to be a massive bruising encounter next week in Dublin.

They've given Franco Smith enough to be angry about when he goes downstairs, to keep everyone's feet on the floor.

Glasgow number eight and player of the match Henco Venter tells Premier Sports: "The hard work is paying off, so we can enjoy tonight and then go again next week.

"Our forwards stuck up to it physically, that's how you play rugby."

Image source, SNS

Tom Varndell
Former England and Leicester wing on BBC Radio 5 Sports Extra

It was a better second-half performance from Tigers, but they were second best in most aspects.

In European rugby you can't be off the boil. Fair play to Glasgow - at points today they were brilliant.

This time the 80 minutes are up, as the ball is kicked into the stands.

Leinster await Glasgow in the last eight.

Image source, SNS

Matt Fagerson boots the ball dead, thinking time was up.

There's still 20 seconds left though... on we go.

The ball is on the dead-ball line as Stafford McDowall grounds it.

No try.

Glasgow think they might have scored a seventh after Stafford McDowall chases after a loose ball.

Glasgow's scrum has been immense tonight and they win another penalty from a dominant nudge.

Adam Hastings kicks the hosts into the corner.

Fraser Brown
Former Scotland hooker on BBC Radio 5 Sports Extra

What Leicester have changed since half-time is their attacking breakdown has been much, much better.

They're on it early, cleaning deep, and taking Glasgow players past the breakdown. It's stopping Glasgow being able to set.

It must have been something they looked at at half-time.

Glasgow do almost find a way through, but Kyle Steyn's attempted to George Horne inside him goes forward and the chance is gone.

Andy Burke
BBC Sport Scotland at Scotstoun Stadium

Glasgow have taken their foot off the gas here, Leicester have started playing some rugby and suddenly the English side are finding some joy.

A 19-point lead should be plenty to see Warriors through, but the home fans wouldn't mind seeing one more Glasgow try just to extinguish any Tigers hopes of a miraculous comeback.

Leicester look certain to score after an interception, but Jamie Dobie does brilliantly to get back in defence and make two magnificent tackles.

The visitors do win a penalty, so the chance isn't gone completely.