The Bees went ahead on the half-hour when Jay Tabb slid the ball home, but they went down to ten men early in the second half when keeper Stuart Nelson was shown a red card.
The Swans were unchanged from the side that beat Chesterfield 4-0 with Lee Trundle once again on the bench.
A Shaun MacDonald shot was deflected for Swansea's first corner in the 11th minute, but Nelson rose high to safely gather Andy Robinson flag-kick.
Swansea should have opened the scoring in the 21st minute when a header from Rory Fallon sent Leon Britton through on goal, but he lifted his shot high and wide with only the keeper to beat.
The Bees took the lead in the 29th minute with a goal created and finished by Tabb. He took the ball down the left flank before crossing and then the Swans defence failed to clear the ball and Tabb neatly fired the loose ball into the corner of the net.
Adrian Forbes replaced MacDonald at the start of the second half as Kenny Jackett's men went looking for the equaliser.
In the 52nd minute Swansea were thrown a lifeline when Nelson upended Leon Knight just outside the area and was sent off by referee Keith Stroud.
The Swans were now well on top and replacement keeper Ademola Bankole had to tip away a vicious shot from Knight.
The equaliser came in the 86th minute when Ricketts cut inside and rifled in a shot into the corner of the net, with the aid of a slight deflection.
It was what the Swans deserved as they had been on the attack for the entire second half, but though they peppered the Brentford goal in the remaining minutes they were unable to snatch victory.