Former boss David Moyes put in bids as he attempted to lure the England left-beck to his new club Manchester United and the prospect of UEFA Champions League football.
But the Toffees refused to sell and Martinez is now looking for the 28-year-old to concentrate on his football now the transfer window has closed.
He told the Liverpool Echo: "We need to focus on our individual and collective targets now, and it will help that we go back to normality.
"Leighton is a fantastic professional and a top footballer. He's an icon for Everton and now is the time he can concentrate on his game and enjoy his football here.
"I think that's what the window does, it gives clubs that instability. In any walk of life when new opportunities come along people think about new possibilities or options in your career.
"That's natural and there is a time for that, but my problem has always been that with the current set-up the window happens while games are being played.
"Now everyone has got to focus and Leighton is one of the big, big players we have at the club."