Goals in each half by Sam Parkin stretched the visitors' unbeaten run to six matches, but King was unhappy about Darius Henderson's penalty which earned Brighton a point.
Referee Mike Thorpe ruled that Brighton's top scorer Leon Knight had been brought down in the box by Stefani Miglioranzi with 15 minutes left.
King said: "Stefani said he never touched him. We feel we have been slightly robbed by a decision." Parkin, a former Chelsea team mate of Knight, put the Robins ahead in the 14th minute.
James Milner, making an impressive debut on loan from Leeds, and Tommy Mooney set him up after a misplaced pass by Brighton's Simon Rodger.
Parkin rounded keeper Ben Roberts to find the net from an acute angle with a shot past a couple of defenders on the line.
Brighton were level within a minute as Swindon lost concentration from the restart. Gary Hart ended a strong run with a low shot from 20 yards, his first goal of the season.
Swindon were the better side throughout a fluctuating contest and they went back in front midway through the second half.
Parkin pounced from eight yards as the Brighton defence failed to deal with a long throw from David Duke.
Two minutes later Mooney, Swindon's leading marksman with six goals, hit the bar with a dipping volley from 25 yards.
There seemed to be no way back for Brighton until Knight, booked earlier for diving when he thought he should have been awarded a penalty, enticed Miglioranzi into a challenge after evading his man marker Jerel Ifil.
Henderson sent Rhys Evans the wrong way from the spot, his second penalty of the season after converting one in the opening day victory at Oldham.
It was an early birthday present for Henderson, 22 on Sunday, and the perfect way to celebrate the launch of his second month on loan from Reading.
Brighton boss Steve Coppell, was relieved with a point. "Very often you play as well as you are allowed and Swindon did not let us play," he said