The Blues have won just twice from six attempts in front of their own fans at St Andrews so far this season.
"The support we get from the terraces is brilliant but we need to give our fans a little bit of a boost, something to shout about and back us with," Clark told the Birmingham Mail.
"If we continue the way we did against Leicester City at home, in terms of the front foot and high energy performance, the crowd will get behind us and help us carry on the momentum we have got to get winning results. That's what we need."
Next up for City is a home encounter against Ipswich Town on Saturday afternoon.