Alex Dunbar went over for Glasgow's first try

With Toulouse going down to Montpellier, Bath now move into the quarter-finals of the Champions Cup, but Glasgow wee inches away victory and a place in the last eight.

Alex Dunbar's try gave Glasgow an early 7-0 advantage but two George Ford penalties kept the hosts within touching distance at the interval.

Richie Vernon's outstanding touchdown moved the Warriors clear again but, despite Finn Russell kicking a three-pointer later on in the second half, two penalty tries helped seal Bath's place in the knockout stages.

Having downed previously unbeaten Toulouse last weekend, 35-18, the West Country outfit were favourites to overcome Gregor Townsend's men and qualify for the quarter-finals.

The Warriors were also suffering an injury crisis with the whole back-row a makeshift combination, but it was the visitors who opened the match on the front foot.

They took an early lead when a superb first-phase attack resulted in a try for Dunbar. Russell converted and the Warriors were 7-0 in front.

That score seemed to affect the hosts who struggled to find the fluency of the previous round. It was also credit to the defence of their opponents who forced them into mistakes.

However, Bath gradually found an element of composure and Glasgow were penalised at the set-piece and breakdown.

Two penalties - one at the lineout and the other at the contact area - duly allowed Ford to reduce the arrears to one point at the interval.

Despite Mike Ford's side seemingly finding some of their fluency, the Warriors remained dangerous with ball in hand and one of the tries of the tournament was finished by Vernon.

Bath did have one advantage over their opponents, though, with their scrum and maul working efficiently. A powerful drive resulted in a penalty try and a yellow card for Alastair Kellock as the hosts went in front for the first time.

Down to 14 men, Glasgow coped admirably as they won the sin-bin period 3-0 through Russell's three-pointer.

Glasgow weren't finished and piled pressure on the Bath line with Sean Maitland stopped inches from the touchdown that would have given the Scots the quarter-final spot.

Glasgow lost a captivating game 20-15, which meant, with Montpellier's 27-26 win over Toulouse in Pool Four's other game, they were within a converted try of reaching the quarter-finals.

"It's really tough for us to take but I couldn't be more proud of the players," Gregor Townsend told BBC Scotland. "I thought they were outstanding."

The Glasgow coach added: "It's very small margins. We were a couple of inches away from scoring a try in the corner.

"We put in a huge effort. The character of the players showed, it came out in our defence and also the way we scored some cracking tries. It could have been a third one. This is why sport and rugby is fantastic to watch.

"I see a team that's improving all the time. We came up short in the final of the Pro 12 last year and I felt we were better today in terms of our belief. When things didn't go our way we showed how we could come back.

"We had some players playing for the first time in positions. Fraser Brown was one of the best players on the field. It is very pleasing when you see players taking opportunities.

Asked how he would lift his players for the PRO12 matches now their European hopes had ended, he said: "We will focus on what we did well today. The second try we scored was out of the top drawer - really good support play.

"Yes, there were mistakes but we know that when we do things well we are a very hard team to beat."

Glasgow scrum-half, Henry Pyrgos, said: "We gave it everything. Bath are a top side. We're hugely disappointed but it's great to see so many Glasgow fans here. It shows how far the club has come in the last few years.

"We want more of this. We want to be getting in to those quarter-finals. There's definitely room for improvement and we'll come back stronger next year. Credit to Bath. They held on."

Glasgow try-scorer Richie Vernon praised the Warriors' team spirit, saying: "We stayed together as a team and we were fighting right to the end. If a few things had gone a slightly different way, we could have easily come away with the result.

"We were under pressure for periods but we felt like we held strong. We had huge belief in the last 10 minutes that we were going to get it."