Stankovic has been rumoured to be seeking a route out of the club, with talk that Internazionale will make a raid for a player that Lazio coach Roberto Mancini considers crucial to his team.
However, a poor performance in the 1-0 defeat to Chievo at the weekend saw the supporters whistle the player.
"The whistling is a really bad thing," said Serbo-Montenegrin team-mate Mihajlovic.
"I know what he is feeling because I had the same problem two years ago.
"Dejan is a really sensitive guy and if things continue in this way then he will under-perform.
"Then of course we would seriously risk losing him."
