Wanderers' first victory of the season came on an afternoon when Blues were their own worst enemy, centre-back Burn misjudging a hopeful clearance up field after just 12 minutes to allow Jermaine Beckford to race through and open the scoring.
Former City midfielder Neil Danns then capitalised on another glaring error, this time from goalkeeper Randolph as he flapped at Liam Feeney's cross, before Bolton held on after substitute Nikola Zigic had given the hosts hope.
Clark, however, was left to rue the fact his side were a shadow of the one which had won their previous three home matches, scoring 11 goals in the process.
"They're just individual errors from two lads who have been brilliant for us all season," Clark said.
"They're human beings, we all make mistakes, unfortunately for the two lads their errors have cost us goals.
"There's no finger pointing at them.
"Our general first-half performance, in terms of not being the driving force we have been in our previous three home games, was the catalyst for the result."
There was controversy in the closing minutes as Birmingham saw strong penalty appeals waved away as Callum Reilly's shot was blocked by the raised hands of Feeney.
"It's a difficult one," Bolton boss Dougie Freedman said. "I can see Birmingham's strong point, his hands are above, but it's so close that the referee has used common sense."
Freedman may well have felt his side got away with the decision.
And Birmingham counterpart Clark was certainly more vocal in his belief that his side were again on the end of a bad decision.
Clark said: "Without a doubt (it was a penalty), there's no ifs or buts.
"In all honesty, that must be at least five now that we've been on the end of that haven't been given for us or given against us."
- Sports & Recreation
- Liam Feeney
- Nikola Zigic