The League One game looked destined to end goalless until Moore was fouled in the penalty area by Scott Wagstaff deep into second-half injury time.
The tricky winger, who had already had Alex's best chance of the game, stepped up and sent City goalkeeper Elliot Parish the wrong way with a thumping spot kick into the roof of the net.
O'Driscoll, whose side slumped to the foot of the table after an 11th game without a win, said: "I didn't think either team deserved to win or lose, so we would have been delighted with a nil-nil to be fair.
"We were resolute and probably had the best chance of the game in the first-half.
"You would've put your money on Jay Emmanuel-Thomas to score one-on-one against the goalkeeper.
"We could've been talking about a great defensive performance and a draw, but it is about a mistake at the death and a 1-0 loss.
"I've seen the penalty and it is soft, but technically the player has been tripped.
"He was going away from goal and (Scott) Wagstaff had no real chance of getting the ball, so he should've just stayed with his runner.
"It is an error of judgement and we got punished.
"We were hard to beat, but we probably didn't work their goalkeeper or back four enough.
"The players are definitely disappointed, but we have no option to move on and take the positives."
Crewe could have had the game sewn up by half-time if they had taken their chances.
A scrappy opening failed to create any openings, but midway through the first half the game sprung into life as Alex created a hatful of chances.
The first fell to Ollie Turton, who burst into the box before seeing a powerful shot saved by City goalkeeper Parish.
Moments later the visitors should have taken the lead with their first chance of the match.
But after pouncing on a heavy touch, former Arsenal man Jay Emmanuel-Thomas could only find the side netting with only the keeper to beat.
Lee Molyneux then called Parish into action again as his shot was saved after some twisting and turning inside the box, before the City keeper produced a stunning save fromMoore, tipping a rasping volley on to the woodwork.
After the break, it was again a story of missed chances, as Molyneux and Turton, along with Chuks Aneke, failed to test the keeper with efforts from in and around the box.
But deep into second-half injury time Moore was fouled in the box and he dusted himself down before firing Crewe to their second successive victory.