Debutant Bellamy, who arrived on loan from Manchester City last week, provided two assists before rounding off the scoring with a wonderful 35-yard free-kick.
O'Driscoll said: "If you can't defend then you don't deserve anything. The first goal was unfortunate and that put us back but if we had scored in the first half when we were the best team it could have been different.
"But when central defenders and full-backs can't be in the right place at the right time then you get what you deserve.
"What we do with the ball ourselves is important but if you can't defend then you won't get anywhere in the Championship.
"We watched Cardiff win at Derby and guessed the team they would put out and for the first half we played well but they were far better balanced when Chris Burke came on and I think he was their best player."
It did not take long for Bellamy to make a telling contribution when he played in Jay Bothroyd who opened the scoring after 36 minutes.
Cardiff doubled their lead in the 62nd minute when Chris Burke, who had earlier came on for Michael Chopra, crossed from the right for Bothroyd to head in his second of the game.
Six minutes later Bellamy found himself in the left-back area and launched a fine ball to set Burke free and he made it 3-0 with aplomb.
When Bothroyd was upended it allowed 31-year-old Wales striker Bellamy to flash home a superb free-kick from 35 yards.
Cardiff manager Dave Jones said: "Craig deserved the applause at the end as I knew he was nervous before the game, but I told him he doesn't carry the club. We are all in this together."
Cardiff City: Marshall, McNaughton (Naylor 18), Hudson, Gyepes, Matthews, Whittingham, Olofinjana, Drinkwater, Bellamy (Koumas 87), Chopra (Burke 32), Bothroyd. Unused substitutes: Heaton, Rae, Gerrard, McCormack.
Doncaster Rovers: Sullivan, O'Connor, Friend (Dumbuya 80), Thomas, Lockwood, Martin Woods, Stock, Mason (Shiels 60), Gillett (Brooker 80), Sharp, Coppinger. Unused substitutes: Gary Woods, Wilson, Hird, Fairhurst.
Referee: N Swarbrick (Lancashire).
Man of the match: Craig Bellamy.
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