The defender has rubbished claims that his switch to the Cottagers was influenced by financial gain but admits he would have preferred to leave Athletic on happier terms
The Venezuelan defender inked a four-year deal at Craven Cottage in April after he rejected the opportunity to renew his contract with the Basque side.
And although he admits that his "dream" was to enjoy success with his hometown club, the prospect of Premier League football ultimately swayed his decision.
"I appreciated Athletic's offer, which was very good, but in the end I thought I would be fooling myself. I was very excited about the Premier League and was eager to go there, even though my dream was to triumph with Athletic," he said in a video message.
"Money did not make the difference. I'd still have accepted less to sample a new league."
Amorebieta follows Fernando Llorente out of the Athletic exit door, with the striker joining Juventus on a Bosman free transfer next month, and the stopper believes their departures have been treated unfairly.
"It wasn't easy to make this decision. It's true that I would have liked to say goodbye on the pitch after helping the team, but the coach decided that others were in a better condition to play rather than myself and that must be respected," the 28-year-old added.
"On one hand I'm grateful that we got to two finals [under Marcelo Bielsa] and that is something hard to forget. But the end of last season was very difficult to take because I was deprived of game time.
"[Llorente and I] made the same decision, and he has been criticised more for it, but hey, it's unfair to receive criticism after the service we have given to the club. We have always tried to help the team over many years.
"[But even after losing top players], Athletic will stay afloat as they have done previously."