Speaking after substitute Shawn McCoulsky headed an 89th-minute victor at a packed Rodney Parade, Flynn said: "This is much better, beating Championship teams like Leeds".
Very few people expected Newport to get the win over Leeds today, especially as the Yorkshire club soundly beat them 5-1 at Elland Road in the First Round of the Carabao Cup earlier in the season.
"I don't want to be winning relegation battles, I want to be winning FA Cup ties and climbing the table".
"I thought we were the better team in the first half, the goal was unfortunate, but we had chances and kept going". The nearest they came to scoring was in the first half when Jimmy Abdou's shot hit the bar.
"It was an outstanding header".
Shawn McCoulsky climbed high to head Newport County to victory over Leeds United.
It was a miserable day all round for the Championship side who were the victims of another FA Cup giant killing.
Top flight West Ham United also flirted with danger at League One (third-tier) high-flyers Shrewsbury Town on Sunday, escaping with a 0-0 draw after being largely outplayed. "They will be at home, more comfortable in their own stadium". Jan Vertonghen added his side's third.
On Saturday 1987 winners Coventry City, who are now languishing in the fourth tier, knocked out Premier League strugglers Stoke City by the same score - a result that cost Stoke boss Mark Hughes his job.
In Sunday's later game, FA Cup holders Arsenal were 2-1 down at half-time against Nottingham Forest.
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