Alex McLeish's £6million summer capture from Valencia completed his first full Premier League game at Arsenal last weekend in place of the injured Cameron Jerome and the Serbia international scored his first top flight goal since arriving at Blues.
Now Zigic is hoping McLeish will keep him in the starting line-up to help him adapt to the demands of the Premier League.
Zigic said: "I was delighted the manager put faith in me by playing me from the start at Arsenal.
"It's taken a bit of time and I'm feeling a lot better and stronger - and that comes with each game you play.
"Hopefully I can keep improving and that Arsenal was the start of a nice long run in the team.
"That is what I would like and it would help me to get better and hopefully be good for Birmingham."
Zigic has struggled to adapt to the pace and power of the Premier League compared to the more technical football he was used to in Spain.
McLeish said: "He has been trying to find his feet but there is loads to come from the big man.
"He has settled in, he is a bit fitter now, and that goal would have been a big boost to him."