The Bairns remain rooted to the foot of the table following the narrow reverse.
However, Kilmarnock's 3-0 defeat at Hamilton and St Mirren's draw with St Johnstone means they are only one point behind their relegation rivals.
Flynn, the league's young player of the month for March, said: "It is a boost that results have gone our way elsewhere but we are more concerned about ourselves. We have to do our job to get out of this situation and I'm really confident we will do it.
"We are obviously disappointed that we didn't get the win against Aberdeen as we came to Pittodrie looking for the three points. Our destiny is still in our own hands and we know with St Mirren and Kilmarnock facing each other next week if we can beat Hamilton then we will be off the bottom."
The Bairns appeared unlucky not to be awarded a penalty just before the break when Flynn fell in the box under pressure from Zander Diamond and Derek Young.
The winger said: "It was definitely a penalty. I can't remember who it was but he was actually on my left foot so I couldn't go anywhere. The ref told Colin Healy that there was contact. I should have maybe been booked for diving if it wasn't a penalty but the referee said nothing to me."
Aberdeen striker Steven MacLean was delighted to score the goal that should ensure the Pittodrie side's SPL survival.
The on-loan Plymouth player said: "Whatever happens to me in the future I just want to do well with the team and get a few goals along the way. It was a massive game and a good goal to win it.
"We answered our critics but to be fair at times we deserved stick. We shouldn't have been in a position where we needed to win like this to get us safe. Hopefully now we can push on and catch St Johnstone."
With the win easing Aberdeen's slim relegation fears, Dons boss Mark McGhee was already planning his summer recruitment drive.
He said: "I think we will kick on in the summer. We have players to bring in. I'm going to stop using the word change because it isn't about players leaving, it is more about strengthening the squad.
"Someone asked me if I was disappointed that the players haven't shown that character more often but I think sometimes they have and sometimes they haven't.
"In their defence they have been exposed a little bit. We picked a side to face Falkirk from 13 fit outfield players. We lost Lee Miller at Christmas who we haven't replaced with a bigger type of striker that Steven MacLean maybe needs to play off.
"The boys have been left under-strength and exposed so it has been hard for them. We have to take that into consideration."