A late, long-range drop goal from replacement fly-half Ronan O'Gara cancelled out an earlier effort from man of the match Stephen Jones and helped preserve Ireland's 20-year unbeaten record in Cardiff.
More importantly, it set up a Grand Slam showdown with England at Lansdowne Road next Sunday - but O'Driscoll admits his side will need to find a major improvement if they are to end their 55-year wait for the championship.
"We're not going to beat England with a performance like that," he said.
"It was certainly sub-standard, and we have a lot of work to do if we are going to beat the number one side in the world."
Tries either side of half-time from flanker Keith Gleeson gave Ireland a 19-7 lead. They held an eight-point lead in the final quarter after a fourth penalty from David Humphreys - but they failed to put the game away.
After conceding just one try in three games against Scotland, Italy and France, the Irish took a backward step by leaking touchdowns to Stephen Jones, Martyn Williams and Gareth Thomas.
"We missed too many first-up tackles," admitted coach Eddie O'Sullivan. "At this level, you pay a big price.
"Wales played very well - which was no surprise to me. I've been saying it all week, but nobody believed me. I feel vindicated - but it was closer than I would have liked.
"They did the same to England but maybe they didn't believe they could beat England. They certainly did believe they could beat us - and they had no reason not to.
"I expected it to go down to the wire - but not that tight."
O'Sullivan felt there was still time to win the game after Jones had edged the Welsh 24-22 in front in the second minute of stoppage time.
"I tried to get a message out that there was at least three minutes left, and that's enough time to get field position and generate an opportunity," he said.