The Belgian international only signed a new three-year deal with Ronald Koeman's side in May and was the subject of a late loan offer from Everton's Premier League rivals West Ham, though that request was rejected.
Speaking after Belgium's 2-1 win over Greece on Sunday night which saw them become the first European side to qualify for next summer's World Cup, the 29-year-old told Greek reporters: "I really wanted to come to Olympiakos
"We tried our best to find a deal that would suit everyone, including President Vangelis Marinakis, who did everything possible and beyond - but Everton turned a deaf ear."
Mirallas is yet to start a Premier League game so far this season but he did start two of Everton's Europa League qualifiers earlier this summer.
The Belgian spent two years with Olympiakos between 2010 and 2012 before joining Everton and admits that he was sad to have failed to seal a return to the Karaiskakis Stadium.
"I am so sad that I have not been home and I hope that will be the case in the near future," he added.
"I would like to thank all Olympiakos supporters for the many messages they sent me. And they must know that I love their club and, as I said before, one day I will come back to them."