A late TMO decision denied the Warriors from taking what would've been a valuable win at Sandy Park in the Champions Cup.
Despite the disappointment of such an agonising defeat, Fagerson insists he and his teammates can be proud of their efforts.
"I'm really proud of the boys after that one," the Scotland prop told glasgowwarriors.org.
"It's a tough decision to take right at the end and it's tough not to come away with the win, but that performance showed what Glasgow Warriors rugby is all about. Some of those defensive sets were superb, and I'm proud of the boys for digging in.
"That's the standard of performance we want to set right at the start of 2024, and if we turn that level in week in, week out then we'll be in a good place.
"We spoke about starting well defensively, and I thought we did that well.
"It was probably those small margins that cost us in the end, Exeter are a good team who will punish you if you give them any opportunities.
"We showed what we can do in attack today, too, so now we need to go out and back that up against Toulon again next weekend."
Gregor Hiddleston made his professional debut for the club and hooker was heavily involved in attack and defence.
"I'm so proud of Gregor," said Fagerson. "Ever since he joined the club, he's given 100% to everything and always takes on board feedback from coaches and team-mates. I thought he gave a superb account of himself today - he hit his lineouts, made himself a presence around the park, and he showed exactly what he's all about as a player.
"He's one for the future, as is Alex [Samuel] and as is Euan [Ferrie], amongst a number of others we've got at the club. All of our young boys are stepping up and showing what it means to be a Warrior, and it's a brilliant thing for the future of this club as well as the present."