The Croatian striker's future is uncertain as his loan deal from French club Nantes is at an end.
However, the supporters have taken to him and directed their chants at manager Owen Coyle, telling him to sign the player up.
Klasnic extended Bolton's lead in the second half after Kevin Davies had opened the scoring.
James McFadden pulled a goal back for the visitors but they have finished the Barclays Premier League campaign poorly with only one win in 10 games.
Birmingham carved out a good chance in the second minute only for Lee Bowyer to be left red-faced.
The midfielder released Cameron Jerome and then picked up the return pass on the edge of the area. Despite being completely unmarked, Bowyer failed to test goalkeeper Jussi Jaaskelainen and dragged his effort hopelessly wide.
Bolton stepped up the pace and Davies found Jack Wilshere, on loan from Arsenal, in the 15th minute. Wilshere played the ball across the face of the area to the unmarked Matt Taylor who looked certain to score but Joe Hart blocked his close-range effort.
A minute later, Gary Cahill set up Zat Knight and the central defender tried to curl his shot beyond Hart, only for it to go narrowly wide.
It was an open game and Birmingham responded with Jerome launching his effort over the bar after a swift counter-attack.
Jerome suffered the same fate in the 24th minute when Roger Johnson nodded on a free-kick from Barry Ferguson.
Bolton, however, made the breakthrough in the 33rd minute after Ferguson had been hauled back for a tug on Wilshere.
Paul Robinson delivered a free-kick into the penalty area and Davies peeled away from Liam Ridgewell to send a header beyond Hart for his ninth goal of the season.
Birmingham hit back and thought they had equalised in the 39th minute when Sebastian Larsson released McFadden.
The Scotland international's shot came back off Jaaskelainen's chest and he knocked in the rebound. But McFadden's joy soon turned to despair as referee Kevin Friend ruled it out for hand ball and promptly booked the player.
Birmingham came close to equalising in the 52nd minute when Roger Johnson found space in the area. His shot was hit straight and true but Jaaskelainen reacted well and pushed it around the post.
Bolton extended their lead in the 59th minute when Klasnic drilled the ball home from close range after good skill from Vladmir Weiss.
Stuart Holden was then given a run-out to raise his hopes of appearing in the World Cup for the United States. He came on for Taylor and sent a shot narrowly wide of the post in the 70th minute.
Substitute Christian Benitez should have pulled a goal back for Birmingham in the 73rd minute but he headed wide at the back post after a cross from Jerome.
The visitors narrowed the gap three minutes later when Benitez went to ground under pressure from Paul Robinson.
Jaaskelainen blocked Benitez's penalty then kept out the rebound from Bowyer only for McFadden to eventually find the net.
Birmingham kept pushing forward but Klasnic almost got his second of the game in stoppage time, only to steer his effort wide.