O'Driscoll said: "You have to give them credit because they've watched us numerous times.
"They flooded the midfield to combat us which I suppose is a bit of a compliment and they were successful with the tactics they adopted.
"We were a bit naive in the way we tried to play against them but they are an extremely professional side and we are learning all the time."
He added: "They deserved their win and it's frustrating for us when things go wrong but there is no point screaming and shouting at players - we just have to learn to improve."
It was Birmingham's first away victory in seven games since Boxing Day against an in-form Doncaster team unbeaten in their previous eight home matches.
McLeish paid tribute to his side and believes they have given themselves a great chance to bounce straight back to the Premier League following last year's relegation.
He said: "We may not be the prettiest side in the world to watch but we have perseverance, resilience and a never-say-die attitude and we showed all those qualities.
"It was important tactically that we played the way we did because Doncaster are a formidable side, particularly at home with the football they play.
"I don't think they played all that badly and if they had got a goal it could have been backs to the wall.
"But we coped with them very well and we have given ourselves every chance now.
"We've opened up a bit of a gap and there is no reason why we can't have the belief that we can achieve what we set out to do at the start of the season."