Glasgow head coach Gregor Townsend refused to point any fingers after his side's hopes of qualification ended with defeat at Northampton.
Warriors were leading 15-12 with time running out at Franklin's Gardens before replacement Harry Mallinder scored a late try for Saints.
That came after Glasgow's Tim Swinson was yellow carded for throwing a punch at a maul, yet Townsend didn't attach any blame to his lock.
"It always hurts to lose in the last minute, but it is the players who put in all the effort and it will be they who are hurting the most after this. They put in a huge amount of effort and I was really proud with the way they stuck to their task," the boss told EPC Rugby.
"Tim Swinson is really disappointed at his yellow card because he knows it cost us. It was out of character for him – he plays tough, but always within the rules. But sometimes when people are hanging on to you things can happen.
"We were in control of the ball at that stage and we could have got a penalty or a scrum. We had just picked up a penalty at the previous scrum and we might have been able to see it out.
"But we always knew how difficult it was going to be to win at Franklin's Gardens. They hadn't gone three games without a win in Europe since 2000.
"We defended really well against their big runners and after a few early problems at the scrum we did well in that area in the end and it was pretty equal. We have shown some good improvement in the last three games, but this will hurt more than the other two defeats."
Last up for Glasgow in the pool stage will be a home game against an impressive Racing 92 side, with Townsend insisting they will not roll over despite not being able to qualify.
"We've still got a game to go in Europe and we will have to see who we play against Racing 92. We'll be playing a quality side and we will be trying to get a win – our fans deserve that," he added.