Umaga, 32, has come under fire from the British and Irish media for the second-minute tackle which saw the All Black centre and hooker Keven Mealamu perform an apparent "spear tackle" on O'Driscoll, who sustained a dislocated right shoulder in the incident.
South African citing commissioner Willem Venter cleared both Umaga and Mealamu of any wrong-doing after Saturday's 21-3 win.
Umaga meant no ill will to his opposite number, and admitted today at the NZ press conference: "While I play hard in all my games, I try and play as fair as I can. That's just the way I am.
"It was an unfortunate incident and these things happen."
Asked further to explain why he did not approach O'Driscoll as the Irish centre lay flat out on the Jade Stadium turf last weekend, Umaga said: "It was obviously dealt with by the people that had to deal with it and I felt that that was the end of it other than maybe having a word with Brian himself person to person. I've never had the opportunity as yet (to do that) but who knows that might happen.
"I asked some of the Lions players after the game (about how Brian was) but again I don't try to do things through the media. We will try to make contact and when we do, we will. It's just how I am."
With the shine somewhat taken off last weekend's victory, Umaga and company have been riled a little by the distractions that the controversy surrounding the O'Driscoll tackle has brought on.
"For the performance we put on (in the first Test), especially our tight-five - they should have received the accolades they deserved," said the 65-times capped Umaga, whose real name is Jonathan Falefasa Umaga.
"But I don't lose any sleep over that. As All Blacks we try and raise standards. I understand we are role models and when that itself is hit I think it's the most disappointing thing for me.
"Everyone's already made their own decisions and we've only got two more days to try and prepare for a game."