Despite the Merseyside club reaching the semi-finals of both domestic cups last season, Martinez was sacked on May 12 after a slump in their league form.
"The team did not perform at all. We won two of our last 11 games. When things are broken between the manager and the players it become difficult," Lukaku said in Knokke at the weekend as he began preparations with Belgium for next month's European Championship.
Lukaku did not elaborate on the breakdown with Martinez nor would he tell reporters where he would be off to next, despite his father saying earlier this month that a move from Everton would be finalised before the start of the Euro 2016 tournament.
"In my head I know where I want to go but I'm keeping that to myself," he said.
"You will know when it is concluded. I have to make a good choice but in my head that has happened already."
Lukaku said staying in England was an option.
"I have played there for five years now, it's my league. But there are other nice clubs. I follow Spanish and German football and I also have something for the Italian league," the 23-year-old added.
"Wherever I go I want to win prizes. During Leicester's title ceremony I was standing just 10 metres from the trophy. I just stared at it for two minutes, forgetting to get on with the warm-up. I thought to myself, I want that."
