The Blues were beaten 4-0 by Barcelona in Gothenburg as the Spanish side ran out comfortable winners.
Barca took the lead inside 33 seconds courtesy of a Melanie Leupolz own-goal and they never looked back from there.
Alexia Putellas slotted a penalty, while Aitana Bonmati and Caroline Graham Hansen also struck before half time too.
It meant Barcelona were crowned champions of Europe for the first time and Bright admitted the loss was a tough learning experience for Chelsea.
“It’s obviously disappointing. We didn’t have the start to the game we wanted,” Bright told BT Sport.
“And I think in these types of games, against these opponents, you can’t concede sloppy goals.
“Listen, they had four chances in the first half and put four chances in the back of the net.
“It’s a massive learning curve, but we are still proud of our journey and what we have achieved.
“We could have had chances and put the ball in the back of the net, but today they just didn’t go our way.
“But, like I said, congrats to Barcelona. They’re an incredible team and deserve it. We will be back better and back stronger for the next time.”
This was Chelsea’s first ever Women’s Champions League final and, despite defeat, they have enjoyed a brilliant campaign.
They have won the WSL and League Cup, and could still claim the treble if they go on to lift the FA Cup.
“It’s massive. We have achieved so much this year,” Bright added.
“It has been a successful year on the back of a really tough journey. There are plenty of positives to take from this game, especially in the second half where we showed our character.
“We did have chances. We just didn’t put them away today and they did.
“The message to fans is: ‘Thank you for your support, as always. Don’t stop believing in us, because we will be back and next time we will do better’.”