The Welsh region trailed 6-3 at half-time but the French club took control in the second half and claimed four tries to record a 32-11 success.
Jamie Cudmore scored and Naipolioni Nalaga claimed a brace before Rhodri Williams' late consolation.
But Clermont had the final word as Clement Ric crossed for the all-important bonus-point try to take control of Pool Four in injury time.
The defeat leaves the Scarlets' Heineken Cup hopes hanging by a thread and they must now win next Saturday's return match to maintain their chances of qualification.
Easterby said: "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.
"We have competed with a side with a far bigger budget and I'm proud with the way the boys dug in.
"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."
Clermont are now in the driving seat in Pool Four and Vern Cotter has challenged his side produce another "massive performance" at Parc y Scarlets to put one foot in the knockout stages.
Cotter added: "The result puts us in a good position moving forward in the group.
"We learnt very quickly what they were trying to do by slowing the pace of the game down and it was very effective for 40 minutes.
"We had to change our game and our tactics were spot on in the second half. We really took the fight to them through the forwards.
"Next week will take another huge performance next Saturday and we will have to adapt our game again because I'm sure they will play the game in another way."