Robson, who had beaten Venus Williams in the opening round, was bidding to become just the second teenager to beat both sisters in the same tournament (after Kim Clijsters).
But although Robson broke in the opening game of the match and held her own at times, Williams simply had too much firepower for 19-year-old.
Robson had also beaten world number four Agnieszka Radwanska, in Madrid last week before losing in the second round to Ana Ivanovic, but although she hit more winners than Williams (17 from Robson compared to the 13 from the American), the world number one was a step up in class and Serena’s superior consistency winning her the match.
Heading into the match on a wave of confidence, Robson broke in the opening game as Williams was a little slow to start; the Brit only just missing her first two chances with aggressive returns before finally snatching the game at the third attempt when Williams netted a forehand.
Williams broke back immediately; leaping all over the at times wayward serve of Robson and firing back a series of vicious returns and, after fending off another Robson break point in the third game, a further break followed for Williams in the fourth, the Brit struggling to find any kind of rhythm on her serve.
Robson finally did hold in the sixth game but by then it was too late for her to save the set, Williams formalising her lead two games later when Robson put a forehand volley long of the baseline.
The early stages of the second set looked set to follow in much the same fashion before Robson found a renewed sense of confidence with a hold from two break points down in the second game.
The match became a much more competitive affair once again and the Brit even enjoyed two break points of her own in the fifth game.
Williams, mindful of the danger Robson posed, saved them both - the first with an ace and the second with a huge forehand – and went on to hold just two points later.
After that disappointment the Brit failed to win another game, Williams breaking immediately as Robson’s serve fell apart with two double faults.
The match ended in a disappointing manner for Robson, as she also served a double fault on match point, but the 19-year-old was far from out-classed by the world number one and can walk away with yet more confidence and another great learning situation under her belt.