The Australian midfielder is set for a $1.55million move to New York Red Bull with Unsworth suggesting the Toffees fans were expecting a departure from the 32-year old.
"I'm not overly surprised," Unsworth told BBC Sport "I don't think his form over the last six months has been what it used to be.
"He's been a fantastic servant for Everton - a bargain buy.
"He's scored many goals but his form has just waned a little bit. I'm sure he goes with everyone's best wishes. I think it suits all parties. Tim has been linked with a move to for the last six months.
"I don't think Everton fans are surprised."