Clark's team made sure their manager will enjoy his 41st birthday when they recovered from the 4-0 thumping at Leeds last weekend to halt Derby's winning run under new head coach Steve McClaren.
Derby had been on course for a third consecutive victory under McClaren thanks to Jamie Ward but substitute Lee Novak's 66th-minute equaliser rescued a point for the Blues.
It was enough to halt a run of five away Championship defeats and Clark said: "If you ask my wife and kids, they hate seeing their husband and dad with a miserable face so 41 tomorrow, I will be sitting around the dining table and they will see their dad smiling for the first time in a while so hopefully there will be some photographs taken!
"I was angry last week, we were hurting but we helped pick each other up during a tough week. We didn't take a day off and worked extremely hard and with each day the sombre mood changed to good spirit and by the end of the week we had smiles on our faces again.
"The players have showed a great maturity for their young age so I was delighted that they have got a reward today. It's the first time this season we have gone a goal behind and have come back to get a positive result so that's an important factor."
Ward tucked away his third goal in two games in the 39th minute when Birmingham failed to deal with a Craig Bryson cross and the Northern Ireland international bundled the ball in at the back post.
Birmingham had already lost danger man Chris Burke with a hamstring strain and their prospects looked bleak at half time but they showed character to come back after the break.
Derby's defence was punished for switching off in the 66th minute when a ball over the top by Paul Caddis was superbly volleyed past Lee Grant by Novak.
McClaren said: "We came across a very dogged and resolute Birmingham team who were smarting from last week and we knew it was going to be difficult.
"I knew it was a game that was all about the first goal and once we got it, I thought we would go on and win but they hung on in there, we created and missed chances but that's football, last week we took them, this time we didn't and that's why it's a frustrating result.
"I am pleased with the performance but I think we lost concentration for the goal. I say we should win those games and score more goals after going 1-0 up but it's early days and it's a case of learning about the team.
"At times we lost a little bit of belief and you could feel that in the stadium and we have to get over that but this team will grow and get better."