The Serbia international has struggled to adapt to the top flight in England since manager Alex McLeish signed him from Valencia during the summer in a #6million deal.
Zigic received a negative reaction from a section of supporters when brought on as a substitute during Blues' last home match with Everton three weeks ago before the international break.
But he responded by scoring his first Premier League goal when given a rare start in last weekend's encounter with Arsenal at the Emirates Stadium.
Now he is hoping to build on that by impressing in front of his own fans at St Andrew's against Ian Holloway's side.
Zigic told Press Association Sport: "I still feel I do have to work a bit harder to win the fans over.
"I do try my hardest all the time and I will continue to do so.
"Hopefully more and more will get on my side as I play better and score more goals.
"But I do feel I have to (produce) a little bit more from myself.
"I want to do well for the supporters. It's always in my mind and I am aware there is a little bit more work to be done to win them over."
Zigic admitted: "It was a great delight to score my first league goal. It certainly has boosted my confidence.
"It was a long time coming but I was delighted to get it. I am really trying hard to get the confidence going and it has helped me immensely.
"When I first came I did find it a bit of a struggle to get to the pace of the game. But the longer I have played the more I have got used to it.
"I have been working hard to get adjusted and I feel it is coming along very well.
"I don't really have a problem with the physicality of the game. It is pretty similar all across Europe.
"I was told it was a little bit more physical here, but I don't have a problem. Again, it's just a case of getting used to it."
Blackpool boss Ian Holloway admitted he is "scared" of Birmingham.
Holloway highlighted McLeish's side as an example for his promoted squad following their brilliant first season back in the top flight. The Blues lost only two home league games last term as they celebrated a ninth-placed finish.
It has been a different story so far this term, with Birmingham's year-long unbeaten home record ended by Everton, while their only win came against Blackburn in August.
Holloway, though, remains a firm fan of the club and their manager.
He said: "Birmingham are one of the teams that I keep talking to my team about. I think the way they play football is a credit to their manager.
"Alex seems a real honest, robust, old-fashioned man who's got values and morals and I love the way his team plays. To be honest, I'm pretty scared of them.
"They really do put a stint in and I think they've been slightly unfortunate this season, but they were exceptional last year, which is full credit to them.
"When you look at the players they've got, I'm expecting a really tough game. When you go to Birmingham City, their fans - if there was a roof on there, they'd lift it off every week.
"They've got a marvellous record at home so we'll have our work cut out. But I'm really looking forward to it. I want to see my lads bounce back from the disappointment of getting no points and see what we can do in this game."
One thing Holloway does not have to worry about, at least for the moment, is injuries, with the Blackpool boss again able to select from a nearly full squad.
But that brings problems in itself and Holloway is disappointed he cannot reward all his squad members with Premier League action at the end of each week.
He added: "With the decent breaks (between matches) you get at this level, everyone seems to be fully fit.
"I'm enjoying that side of it and it's very difficult to look all my lads in the face at the moment because they're all doing so well in training.
"I'd love to give them all a game but I can only pick 11."