Milan finished third in Serie A last season following a miraculous recovery in the second half of the campaign whilst they also reached the last 16 of the Champions League, eventually being defeated by Barcelona.
But Galliani says it is vitally important they finish in the top three again and is hoping for an extended run in the Champions League.
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“So we go into the new season without any psychological issues.
“Our goals are to get back into the Champions League, to try and go as far as possible in that competition and win the Coppa Italia.
“To finish first, second or third is crucial. Everyone knows that the economic advantages of the Champions League are huge.”
Galliaini also revealed they are still in talks with Santos over the transfer of Robinho. The Brazilian has been linked with a move back to his homeland but no deal has been finalised yet.
Milan are looking to acquire the services of Fiorentina's Adem Ljajic and CSKA's Keisuke Honda as replacements for the 29-year-old.
He added: “Negotiations are underway with Santos. The boy [Robinho] wants to go home.
“There are still some things to be sorted out though.
“Ljajic? There have been some rumours, and I will not deny it.
“Honda? We hope to get him to Milan in January.”