"It was just reward for all the effort and quality," said Flynn.
The game had been billed as the battle between two managers who both hail from the same part of Newport, with Flynn's counterpart, Tony Pulis, now getting the chance to return to his home town for the replay.
"Obviously there has been a lot of talk about me and Michael (Flynn) but it was a game and once the game starts you want to win," said Pulis, who thought his side had done enough to progress after Daniel Ayala put Boro into the lead early in the second half.
But Newport, who beat Premier League side Leicester City in the third round, scrapped hard for the equaliser, which eventually came deep in injury team when Dolan scramble the ball home.
"We should have dealt with that one (the goal) a little bit better, they had a good chance before that too. You have got to give them credit. For 25-30 minutes we completely dominated and you have got to create chances and take opportunities, and we didn't finish them," said Pulis.
"There has been a bug around the place and one or two players and staff have suffered but I don't want to take anything away from Newport today, they kept it going until the last minute and I am disappointed we conceded late on."
Pulis said he was delighted with the debut of John Obi Mikel, the former 32-year-old former Chelsea midfielder who signed last week after being released by Chinese side Tianjin Teda.
"John Obi Mikel did smashing, that was his first game for a long time. He is so composed on the ball, he lifts the rest of the team, he is that type of player," said Pulis.
(Reporting by Neil Robinson; editing by Tony Lawrence)
