The Irish broke an 18-year jinx by defeating Scotland 36-6 in Edinburgh last Sunday to open their RBS 6 Nations campaign in style, but the Lions centre is only too aware of how dangerous complacency can be.
With a tricky assignment up next against an Italy side buoyant after their 30-22 win over Wales, O'Driscoll said: "Obviously you have to say it is a big monkey off our backs to have won there. It was a long time coming but, having said that, it was a win we felt we deserved.
"But we're not patting ourselves on the back and telling each other we're great.
"It's more a case of move on and move upwards if we want to go on and compete in this competition.
"Last Sunday would be pointless if we went and lost this Saturday, so you must take each game at a time and put the last one behind you.
"We'lll take the confidence from winning that game but there's no point in dwelling on it."