The Ukrainian champions have seen six players fail to return from Sunday's friendly with Lyon due to ongoing politicial tensions in the country.
Alex Teixeira, Fred, Dentinho, Douglas Costa, Facundo Ferreyra and Ismaily are the players currently absent, while Shakhtar are unable to play in Donetsk.
However, following Tuesday's Super Cup success against Dynamo Kiev at the Lviv Arena, Palkin confirmed Shakhtar would be based in the city for the coming season.
"Hand on heart, [the support was] not quite equal. But, I think, we will correct it in the future," he told the club's official website.
"And it will happen in Lviv. Because we plan to play here our home games in the domestic league and the Champions League."
The CEO also spoke of the pressing need to convince Shakhtar's absent players to return to Ukraine - stating they should not be afraid of returning to the country.
"Now we have the period of persuading them: it's OK in Ukraine, they can play here, reside and live a normal life," he added.
"This is the main task for today, because many people are scared. In the future, I hope, everything will improve and get back on track. If not, there are other mechanisms to be involved."
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