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Clermont outscored their hosts by three tries to two but an unfavourable penalty count and two turnover tries saw Stade march on to Cardiff.
"There were a few critical errors that got them over the line," said Cotter, following a up-and-down encounter in the French capital.
"I was pretty pleased with our attitude - we went out there and scored three tries - but we didn't control the end of the game in the way we would have liked.
"We scored the first try and got in front and then we let them back into the game with a couple of silly errors - they got an intercept pass when we were attacking.
"That was the story of the whole night for us really: as soon as we got in front, we'd make a mistake and they'd get back in front.
"We gave them a nine-point lead but, credit to our boys, we recovered from that but then we gave them another 10 again. It was one of those nights and we've just got to move on as quickly as we can."
While Cotter admitted that there were elements of the performance didn't impress him, the New Zealander couldn't fault his team's effort and commitment.
Stade went into the game knowing defeat would bring their season to a premature end due to their failure to remain in contention in the Top 14 and there were plenty of critics who suggested the hosts would simply want the win more than Clermont.
There's no doubting that Stade fought tooth and nail throughout but Clermont matched them and could have snatched victory if Morgan Parra had been successful with his conversion of Jamie Cudmore's 77th-minute try.
If the France scrum-half had slotted the extras from 15 metres to the left of the posts, he could then have taken on an even later long-range penalty rather than being forced to kick to touch.
In the end, Clermont came up just short, but Cotter will be hoping his men will have learnt from the experience as they look to successfully defend their French title over the coming weeks.
"It's disappointing. The players are disappointed," added Cotter.
"We would have liked to have gone to a final. That's not the case now.
"It went right down to the wire. It went to the last play. Both teams wanted the victory and we'll be in a similar situation next week against Toulouse.
"We've got to learn from tonight and get on with things next week. It's just about how we react if we find ourselves in a similar situation.
"It's now a matter of bouncing back in the Top 14 competition. In these types of games you learn a lot and, with very little rugby in front of us, every minute and every part of the games that are in front of us will be important, just as it was tonight.
"We're not hiding the fact that we're disappointed. That frustration and disappointment will be put into improving our game and trying to make it stronger for our next encounter."
