The Millers were held to successive home draws against Abbey Hey and Barnton.
It leaves them trailing NWCFL First Division South Leaders West Didsbury & Chorlton by three points.
“The Abbey Hey game was a missed opportunity. We should have won the game, it wasn’t the greatest of performances, but we played well in parts.
“We missed two great late chances at the end to go 3-1 up, they were open goals.
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“They had a free header at the death and could have won it. A point is not bad against them but I was disappointed not to win it.
“Barnton didn’t play like a team at the bottom end and were worthy of a point.
“But we were poor in the second half and did not manage the game. We were 1-0 up and 2-1 up and should have won.
“Barnton never gave up and gave it a good go and got what they deserved.
“We had a good goal disallowed and they should have had a lad sent off at 2-1. We had a chance to make it 3-1 and that would have been it.”
The damage has been limited after leaders West Didsbury picked up just one point from their last two games.
But, despite feeling the frustrations, Birch is content with where New Mills sit in the table.
“It is more frustrating with West Didsbury losing at the weekend,” added Birch. “We failed to capitalise on it.
“If we had got the points in midweek and at the weekend we would have been top of the league.
“But we are three points off the top of the league. If I was offered that at the start of the season would I have taken it? Probably.
“We knew teams would drop points, those around us will drop more points, we will drop more points.
“It is a difficult league and teams can beat anyone in this division.”