Clark took the reins from Chris Hughton over the summer but has not enjoyed the best of starts to his tenure despite a promising pre-season and a convincing 5-1 Capital One Cup victory over Barnet in his first competitive fixture.
Blues salvaged an injury-time draw at home to Charlton in their league opener before disappointing defeats at Sheffield Wednesday and Watford was followed up by a cup exit to League One Coventry in midweek, with almost 4,000 travelling City fans booing at the end of the encounter.
Clark revealed: "I've said to the players, we've got to turn it around. There's only us who can do it. I'm not giving up, I'm at a fantastic club with fantastic people, brilliant supporters and I promise them I'll turn it.
"It's not been an easy time for us. It's not been an easy time for my family either because I've moved them down and we can't get out the house, I dare not go out. I don't like to lose, I get very embarrassed if I'm walking around the streets because I feel as if I'm letting people down.
"It's probably the biggest test of my managerial career and I'm not going to shirk the challenge, I'm not going let the supporters down. I'm proud to be their manager and I want to be the one who delivers them success and I can be. I'm determined, I will work every hour, I'll do whatever I've got to do to get it right. Saturday (against Peterborough) we need to win no matter how, It doesn't matter how we do it we need to win the football match."
