The Dutchman picked up a second yellow card for a foul on James Beattie, as the Underhill outfit earned a vital point to lift them out of the League Two relegation zone
The Dutchman earned a second yellow card in the 86th minute after catching the former Everton forward - who was making his Accrington debut - with a late tackle.
Romuald Boco had put the visitors 1-0 up shortly after half-time, before Mark Byrne levelled from the penalty spot.
Davids' early exit brought an end to a bad week for the former Netherlands international, after he recently swore on live television.
The 39-year-old, who once starred for Italian giants Juventus, holds the role of joint manager at Underhill alongside Mark Robson.