Ramsbottom have now gone six games without a win now as they failed to capitalise on the many chances that they created.
On 36 minutes, the Rams were dealt the worse kind of fate when Squires Gate earned themselves a penalty after Cabbar Bagdagi brought down Paul Ryan just inside the area.
Matty Muscroft sent goalkeeper Martin Campbell the wrong way and put the seasiders one-nil up.
The second-half saw the Rams equalise when they were awarded a corner.
Matt Eckersley floated in a perfect cross that the keeper could only spill and Andy Sensale managed to push it over the line.
But Squires Gate went back in front through Andy Harvie with a perfect shot into the bottom corner.
In the dying minutes of injury time, Rams substitute Matt Ward saw his shot come back off the crossbar.
Brendan O'Shaughnessy was sent off late for Rams.