Ireland eventually scored five tries in the Italian capital despite trailing 6-0 until the 19th minute.
"We were patient and knew we would have to wait to break them down before taking our opportunities," said O'Driscoll, who appears to be finding his form just three-and-a-half months out from what would be his third Lions tour.
"We are pleased but there is still a lot of graft to put in before the England game."
Like O'Driscoll, Kidney felt Ireland's ability to stay calm despite their early deficit allowed them to produce a convincing performance for the final hour of the match.
"Because there was so much competition at the breakdown we were conceding penalties which put them in front," explained Kidney, who is enjoying his first Six Nations as his country's head coach.
"Our first try was well taken by Tommy (Bowe) but we were a bit fortunate to get it. That try was a huge lift for us.
"I thought we were very patient after 20 minutes.
"In the first 20 minutes we were pushing it a little bit and Italy had us under enormous pressure."
O'Driscoll's sentiment of a tougher job to come in a fortnight's time was also echoed by Kidney, who expects a stern test when England travel to Croke Park on February 28.
"I thought that they (England) improved 300 per cent from the previous week," said Kidney, having seen England run tournament favourites Wales close in Cardiff on Saturday evening.
"They've really come on.
"It's important with the new agreement that they have a week off and it gives Martin (Johnson) a chance they didn't have heretofore to improve for two weeks time.
"Ireland-England games you look forward to in a kind of masochistic way. You know how good they are.
"The size of the challenge has improved enormously and they'll be eyeing us as a target."