It was Bower's first game in charge since returning to the club two weeks ago. He has brought in several players to bolster his squad and coming after an 8-0 defeat by Brackley, it has lifted spirits at the Horsfall Stadium.
"Delighted with it obviously," Bower told the Avenue OS.
"We've been in for a couple of weeks now, we're not in a great position in the League and things have not been going too well.
"But we were a lot more solid and physically strong today in comparison to earlier this season.
"We got the first goal from a set-piece and a fantastic second goal.
"It's been about making them work a bit harder, we're a bit more resolute, a bit more experienced.
"We did have a period in the second half with a few tired legs but with that experience we could put ourselves in the right position and get that ball up the right end of the pitch to relieve that pressure. I thought we did that really well.
"For a team that lost 8-0 last game, to get that sort of reaction was a fantastic achievement."
Bower mentioned the performance of keeper Joe Green.
"Towards the end of the game when a lot of balls were coming into the box, he was really dominant and it took a lot of pressure off the defence. He made a couple of good saves for us."
Bower was asked about Hereford's penalty when the referee decided Tom Owen-Evans had been brought down in the box.
"We've seen that tackle three or four times in the second half when the defender comes across, plays the ball and takes the man as well.
"I was surprised he gave the penalty."