The Sulphurites found themselves 2-0 down to their title-chasing hosts inside 50 minutes, and although they finished strongly, they were unable to get themselves back into the contest despite Jay Williams' late header.
"I was very frustrated for the first 35 minutes of the game, I just didn't think we applied ourselves in the manner that we had prepared for. We were wanting to take on a top-three side and be aggressive and on the front foot, but it was a limp start from us," Weaver reflected.
"It looked a game too many for a few, we conceded two poor goals and when we did get the ball, we just seemed to shell it forward.
"Yes, you've got to mix it up, but you've got to show some bravery on the ball and too many pretended to want the ball and didn't really apply themselves like we know they can.
"Maybe it's new territory, a top-three team, maybe the [windy] conditions affected the mindset and we were not as positive or brave on the ball, but whatever the reason may be, it's just an excuse. This was a good pitch here today and we should have played better.
"When we applied ourselves and worked to the game-plan there were signs that we could get into areas where we could hurt them. It was just that little bit of quality that you need to get back into the game.
"Overall it's a disappointing day. Despite the territory and possession we did have, we didn't really test their keeper enough, and thus we didn't deserve to win the game."
Forest Green took the lead on 22 minutes when Harrogate failed to clear their lines following a Nicky Cadden free-kick, Chris Stokes firing through a crowd of bodies to beat James Belshaw at his near post.
Right-back Kane Wilson started and finished the move which saw the home team go two up, exchanging passes with Jamille Matt on the edge of the box before firing across Belshaw from close range.
Substitute Williams nodded home George Thomson's left-wing corner in stoppage-time to give the Sulphurites late hope of salvaging a point, though that was as good as it got for Weaver's troops.
Defeat sees Town drop one place to 11th in the table, but they now find themselves eight points shy of the division's final play-off spot.