The home side dominated for long stretches and might have enjoyed a more comfortable victory but for some resolute Lions defending with the tourists' only try coming from O'Driscoll in the closing stages.
The Irish centre told Sky Sports: "We're very disappointed. Sitting in the dressing room and looking back we feel that we weren't worthy of winning the game.
"They had all the possession and it's difficult to score from you own half.
"We didn't play any of the rugby in their third. The majority of their rugby was played in our half. You can't play rugby in those areas and expect to win."
O'Driscoll admitted the result meant Wednesday's meeting with Wellington will be played under extra pressure but the Leinster man is confident the Lions can turn things around in time for the first Test on June 25.
He said: "We've got to stay really tight and there's going to be all sorts of comments in the press and the Wednesday side have to stand up and show what we're really worth.
"Two weeks is a long time when you're on tour and, like I said the Wednesday boys have a challenge to get us back on a roll.
"It's not the end of the world in that it's better losing now than in two weeks."