A major FA Cup fourth-round upset looked like being on the cards in South Wales until Harry Kane tapped home at the back post in the 82nd minute, meaning a lucrative replay for Newport at Wembley early next month.
Flynn was proud of the display produced by his players, but admitted that it may well be an opportunity missed.
"I'm gutted if I'm honest because we conceded so late in the game," he told BBC Sport. "But they are a quality side and in the second half we couldn't really get at them.
"The first goal was important for us but it's something else for the club to look forward to. We were nearly there. We could taste it but we switched off one minute and Harry Kane scored.
"The big boys can punish you. That's why they're getting paid so much and that's why they're playing in the top leagues. It's going to be a tough ask at Wembley, but we'll go there and give it a go and you never know."
Newport, ninth in the fourth-tier standings, return to league action on Tuesday night with a trip to Lincoln City.