Blues took another step towards survival with a 1-0 win over Bristol City to condemn their hosts to relegation.
Clark is taking nothing for granted and is determined to get the three points when Leeds visit St Andrew's.
"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," said Clark.
"We owe them a big performance because we have not been at our best in recent home games.
"Tonight my two centre-backs were fantastic. We had to defend well because we didn't pass the ball as we can.
"Our good away form has been the result of being solid as a unit and that was evident again in this match.
"Now 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."