The Blues eased any relegation worries they had with a 1-0 victory over Bristol City, which condemned the Robins to playing League One football next season.
"We are not quite mathematically safe and it would be nice to take care of that with a good result in front of our own fans on Saturday," Clark told reporters.
"We owe them a big performance because we have not been at our best in recent home games.
"I want a really big effort at St Andrew's because there are a lot of positives to take from the second half of our season."
Birmingham are 12th in the Championship, six points clear of the relegation zone.