The 30-year-old has accepted an offer to join Austria Vienna and will move on a Bosman transfer.
"As far as I'm aware, Thomas is going to Austria Vienna at the end of the season and has agreed terms with them," said Levein.
"It's no secret that I like Thomas. The fact he plays every week and in a number of positions shows there's no doubt he'll be a loss to the club.
"I'm going to have a problem at the end of the season, because somebody's favourite player is going to be leaving.
"It could be any of the six players we've got out-of-contract and I know I'm going to have disgruntled supporters.
"My big test is to make sure I keep some of these players and make sure the guys I bring in quickly make the supporters forget about the lads who have left."
Amongst the other players who are out of contract at Tynecastle in the summer are Steve Fulton, Robert Tomaschek, Stephane Adam and Tommi Gronlund.
