The visitors were punished for switching off as Jordan Rhodes he notched up his 100th career league goal with his brace at Ewood Park.
Rhodes latched on to a loose ball after a Morten Gamst Pedersen cross was not cleared and he later raced on to a long pass from Danny Murphy to dispatch the second.
O'Driscoll said: "In this division set-plays play a massive part to concede from a second phase from a corner is disappointing but apart from that at half-time, we felt okay.
"I thought we could score a goal and were terrific at the start of the second half, but Danny Murphy hauls a ball back and we're two down.
"It's the first time we've had this sort of problem to solve but felt we went about it the wrong way.
"Lots of endeavour but we lost our shape and structure and you can't do that in this division, but for an hour I thought we were terrific."