O'Driscoll's men dominated most of the game and a second-half goal by Scott Wagstaff looked set to earn them a first league win of the season.
But Flint's dreadful back pass was pounced on by Vale substitute Lee Hughes, who took the ball around Elliott Parish to net the 90th-minute equaliser.
O'Driscoll said: "That was our most complete performance of the season and we deserved to be going home with three points.
"But we aren't because of an individual mistake and we have to take the positives out of the game, keep working hard and move on.
"Aden will have to learn from it. He's 24 years old and he can't let a mistake like that affect him. He's got to pick himself up and bounce back from it.
"It's disappointing but I'm also pleased with how we played. For those people who were moaning and groaning there were signs that we are getting there.
"We are in transition and improving. It was nice to put in a performance where all the units have worked well together.
"We've hit a post, created a lot of chances and would have won if we had kept a clean sheet. We've made a crucial error at the wrong time and they have capitalised on it. It was their only real chance in the game and they have put it away."