London: Victory gave South Africa the three-match series 2-0 after they’d crushed England by an innings and 12 runs in the first Test across London at The Oval before the second Test in Leeds was drawn.
Smith was wearing a shirt bearing the words 'We miss you Bouch', a tribute to former South Africa wicketkeeper Mark Boucher who was ruled out of the series after suffering a career-ending eye injury in a warm-up match against Somerset in Taunton.
"This was meant to be his 150th Test. He's been such an integral part of getting us to this point and been an integral part of the team for so long," said Smith.
England, set an imposing victory target of 346 to win, were bowled out for 294 on Monday’s final day, with man-of-the-match Vernon Philander taking two wickets in two balls to end the contest as he finished with an impressive innings return of five for 30.
"The way it finished was perfect for us," said Smith, who led South Africa to victory in England in 2008 — the last time England lost a home Test series.
"The biggest thing for us is to win when it’s tough and you are not always ahead of the game.
"We came here with England the number one team in the world. They are an outstanding team in their own conditions and to beat them at home is one of the great achievements of my career."