The Brazilian joined the Merseyside club for around £21m after a successful spell with Napoli.
The midfielder will miss Everton's next three fixtures after their appeal was turned down.
“We had a really bad decision against us which we had an apology for but apologies don’t mean points."
"These players with character are normally in the top sides, but we have to find them."
“My thoughts are to remain at Everton for as long as possible. It feels good, I feel at home here."
Allan has signed a three-year contract with Everton for an initial fee believed to be around £21.7million.
Man Utd's contingency plans this summer seem to focus on Bournemouth, while Leon Bailey could replace Leroy Sane...
Flamengo and Sao Paulo have also been linked with moves for Allan, who has never made an appearance for Liverpool.
Allan says he is determined to play for Liverpool one day despite difficulty landing a work permit.
Jurgen Klopp says his initial reaction to seeing Allan Rodrigues de Souza in training was ‘oh my God’.