Joe Day saved Tyler Walker's spot kick before Matt Dolan netted the decisive penalty after a thrilling game had somehow ended 0-0 after 120 breathless minutes.
READ THE MATCH REPORT HERE“It is a fantastic achievement,” smiled Flynn.
“What an amazing thing these players have gone and done. I thought we were excellent today – absolutely superb and we should have gone three or four up first half.
“Second half they came back into it a little bit and had a few chances of their own. Then extra-time was like a basketball game – end to end. For the neutral it must have been brilliant.”
Flynn said he was calm when the game went to a shoot-out.
“It's one of those situations that what will be will be. But I had full faith in these players,” he said.
“I asked them what position they wanted take the penalties in, every single one of them go the position they wanted, and every single one of them scored.”
Keeper Day had a superb night and Flynn said: “Joe was fantastic. He made a couple of really good saves and then saved the best until last. He's been a rock for us.”
Now Newport prepare for Wembley and he added: “I just said to the players – here is your challenge. In 13 days time do we want to be Newport County AFC in League One?
“It is an unbelievable achievement and I cannot praise these players and my staff high enough.
“We have got through a lot of challenges. We have a board who support things as best as they can and a fantastic group of supporters who've stuck with us through thick and thin.”