Chester manager Calum McIntyre said that Hereford's late goal was 'a great strike'.
Luke Haines's shot from 30 yards gave the home side's keeper little chance.
But McIntyre was disappointed to have conceded with minutes left.
"I am really frustrated it is a late goal," he said.
Chester probably shaded the first half but Hereford looked more likely to score as the game went on.
"It was two good teams out there. Both play a particular type of football that probably meant a decent game. But we are disappointed not to have taken one of those chances.
"We created chances, worked with the ball and limited them to one chance
in the first half. So, we congratulate them on what they have been able
to get out of the game but reflect with real positivity that we have
been able to dictate against a really good side at home and put on the
type of performance that we would want - but not got anything to show
for it."