Their message was clear, however: this was not the end, but the start of a club on the rise.
"We have created something special, you can see that with the crowds that came to this game and that is down to the way the way the players put so much effort into the way they performed on the field," said head coach Gregor Townsend.
"There were a lot of lessons we took from losing semi-finals and they have made us a stronger team. Now that we have got to a final, we have to handle it better next time.
"It was a wonderful occasion; the noise and the number of Glasgow supporters there, it was a fantastic day. The game itself will have been great for the neutral but there were times when we needed to have more control, more patience in our play.
"I don't think the players were overhyped but maybe the element of control was missing for whatever reason. We did really well leading up to the 22 but did not finish those opportunities. We rushed things at times.
"We knew we had to play our best game of the season to win and did not do that. We had moments of ascendancy in the first half, we were breaking tackles, but on two occasions we got into the 22, we didn't execute and we have been very good in that area."
It was a similar message from captain Al Kellock, who has challenged the players to use the experience of losing this final to go one better next year, both for the players' own pride and to repay the fans.
"The support was unbelievable - unbelievable, from the stand, from the point of view of the messages we have had over the last few weeks" he said. "We really wanted to win to repay them all but we can't let the good work slip because we lost.
"We have to keep pushing forward. Though we lost this final, if we win one next year - you would take that. The emotion I am trying to force to the front of my mind is pride in the effort.
"What a two weeks it has been. The was the pride in the effort to win the game against Munster, the fans on the way into the ground were incredible.
"Though I am trying to force that to the forefront of my mind, it makes it hurt even more. We have to push forwards, we have to get better. Gregor spoke about how proud he was of the effort that has gone in.
"We will analyse the game at some stage. We spoke in the changing room of how to use this again the way we used the semi-finals to push forward. I can say at the moment that it hurts to lose a semi-final; it hurts more to lose a final."
Kellock conceded that Warriors' main problem had been the error count. When chances came and cool calculation was needed, Glasgow became hot-headed; when they needed to calm down and cut out the mistakes they became frenzied.
"I believe we pushed them really hard, There were a few key points in the game where we needed to get the break," Kellock added. "Though the scoreline looks comfortable, if we had had the right break at the right time we could have gone on to win.
"On the day, though, the better team won and that is hard to take because we went out with the intention of playing the way we wanted to play and we did not execute. But we have to be proud of the effort that got us here."