However Clermont raced away in the second half to a 32-11 victory, despite a late consolation try from replacement Rhodri Williams.
The result knocked Scarlets down from top spot to third in Pool 4 and Easterby believes his side must not be afraid to front up against the best Europe has to offer.
"We have competed with a side with a far bigger budget and I'm proud with the way the boys dug in," he said.
"But ultimately digging in is not enough in this competition, you have to be better.
"We have to be harsh on ourselves because when you have opportunities you have to take them.
"We can learn a lot from this performance and our young players would have taken a huge amount from it.
"The effort was there for everyone to see but I'm disappointed we offered them a bonus point they didn't deserve.
"They're a fantastic side when they have momentum and we defended our hearts out but they weren't a bonus point win better than us."
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