Lee Novak powered home unmarked from 10 yards just before the half-hour mark for his third goal of the season, handing the hosts a deserved half-time advantage at St Andrew's.
But the flow of the game changed after the restart and Rovers battled back to grab a share of the spoils courtesy of David Cotterill's 30-yard thunderbolt 12 minutes from time.
And Clark rued what was a slack second-half showing from his charges until the late leveller shook them back into action.
"It's another point, it keeps our unbeaten run going, but I feel it's an opportunity lost," he said, as City went four games without defeat.
"We put ourselves in a great position and then second half, for some reason, we didn't continue what we did in the first half.
"They started dominating the game a little bit in terms of getting at us a bit too easy, and then we give a goal away that we shouldn't do.
"It's a wonderful strike, I'm not taking anything away from that, but they had too many unforced passes leading up to it.
"And then when they score we've got something to play for and our lads go back on the front foot and cause lots of problems, and then Doncaster don't cause us any more difficulty after that.
"I've said to the players, why not do that from the 46th minute? Go for 2-0, go for 3-0."
A draw was no real surprise considering Doncaster went into the encounter having triumphed just once away from home in eight attempts this season while Blues had racked up just two league victories at St Andrew's.
And so it proved as two struggling sides, who started the day separated by just one point and one place towards the wrong end of the Sky Bet Championship table, finished with a point apiece and both still to record back-to-back league wins this term.
A point was enough to end Doncaster's eight-match losing run against Birmingham, stretching back to 1954.
And boss Paul Dickov was purring over Cotterill's cracking equaliser.
"It's a fantastic strike," he said. "We know David's got that in his locker from the goals he scored last year.
"It's something he practices a lot, technically he's very good.
"He's a had a few this year which have gone wide and over the bar so I'm delighted for him."
In contrast to counterpart Clark, Dickov looked back on an improved display from his side after the break following a disappointing opening 45 minutes.
"We don't want to get beat in games and limp off the pitch at the end of it. If we're going to get beat, at least get beat having a good go," he said.
"I didn't feel as though we did that well enough in the first half.
"My players know what I'm like as a manager, if they go out there and have a right good go then I'll back them all the way - win, lose or draw.
"But I keep saying to them if you do have a go and try to do the right things then you've always got a chance of getting points."