They Bucks arguably had the better chances at a sold out Edgar Street but it wasn’t to be as Hereford of the Southern League progressed at their expense.
United’s cause wasn’t helped by a straight red card for Jon Royle as John Mills went on to get the winning goal and leave over 700 Telford fans heartbroken.
Edwards told the Shropshire Star that they had enough chances to be the ones heading into the hat for Monday’s draw.
"The sending off changed the complexion of the game," said the Bucks manager.
"I don't think we started the second half particularly well, but I didn't think they were the better team at that point.
"It lifted the crowd and obviously they had the numerical advantage, and they got the goal - the all-important breakthrough.
"I thought in the first half we were excellent, the better team. We played some really good football and had some excellent chances.
"We didn't take those chances. Football is ultimately about scoring goals - they did, we didn't."
He said to the Star: "I'm incredibly frustrated.
"There was some good performances but Cup football is about winning, and we didn't do that."