Head coach Gregor Townsend spoke of his pride in his players as they were squeezed out of the European Champions Cup by Bath at The Rec.
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," Townsend told BBC Scotland.
"I thought they were outstanding."
Warriors, who beat Bath 37-10 in the first round of matches last October, came desperately close in the final minutes to scoring a third try to add to well-worked scores by Alex Dunbar and Richie Vernon, one in either half.
Glasgow's Tommy Seymour almost broke through and winger Sean Maitland was halted half a metre from the try line in the dying seconds by Jonathan Joseph.
But Bath, who had forced the visitors on to the back foot for much of the second half. held on to their five-point advantage.
Townsend 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.
|European Rugby Champions Cup Pool 4|
"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."
Glasgow led 7-6 at half-time, and at various points throughout the game, with the score between the two French sides in Pool Four see-sawing, they topped the table and looked as if they might go through as pool winners.
Indeed, when a Finn Russell penalty put them 15-13 up and then Russell and Maitland somehow prevented Anthony Watson from touching down, Townsend and the travelling fans must have thought it was their day.
Yet Bath immediately scored their second penalty try, which they converted, to put them in charge.
Asked how he would lift his players for the Pro 12 matches now their European dreams had ended, Townsend 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 try-scorer Vernon praised the Warriors' team spirit.
He said: "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."
And his team-mate Henry Pyrgos, who made way for Bath-bound Niko Matawalu with 11 minutes to go, added: "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."