India on Sunday rode on a superb bowling show to thump South Africa by eight wickets to become the first team from Group B to enter the semi-finals of the tournament.
Disciplined Indian bowling bowled out South Africa for 191 runs in 44.3 overs at The Oval. India chased down the target in 38 overs with eight wickets to spare.
Smith opened up on his team's form and current performance and said the Proteas missed the spark in the prestigious tournament.
"I left the ground on Sunday feeling as many South African fans will be feeling. Disappointment that the team haven't managed to recreate the form and the brand of cricket that have seen them be so successful in white ball cricket over the past 12-18 months," Smith wrote in a column for International Cricket Council's website on Sunday.
"I still care deeply about the environment that I spent so much time building as a player, and it hurt to see such an unrecognisable South Africa performance.
"The side have been missing that spark, or that intensity to their play that characterises South Africa cricket," he added.
The veteran batsman also expected his side's top order batsmen to put pressure on Indian pacers from the onset of the game.
"What I would have liked to have seen from the guys at the top of the order is, at least, an attempt to put Jasprit Bumrah and Bhuvneshwar Kumar under pressure," Smith said.
"Anything to put them off their game and bring their plans in to question. Our approach was far more conservative, and if you're going to play that way, you can't afford the calamities that unfolded in terms of the two mid-innings run outs. They will kill any momentum you have, and suck the energy from a dressing room," he added.
Smith also emphasised on the mindset and approach a team needs to have before heading to a crunch match.
"Mindset, and your approach to the game, are those one percent factors that make the difference at this level. When those factors are not there, you pay the price and it's the team's approach that has been the missing ingredient," the 36-year-old said.
"If you're ever so slightly off the boil that will translate to the performances on the field and often it just doesn't look right. Since the team have started against England in May, it hasn't looked right to me as an observer," he added.
Smith also spoke about middle-order batsman Faf du Plessis, who was involved in two vital run outs, which also cost them the match.
Skipper AB de Villiers (16) and David Miller (1) were sent packing in the 29th and 30th overs, respectively, which saw South Africa reduced to 142/4.
De Villiers was run out when he ran for a single for du Plessis but a throw from Hardik Pandya at the wicket-keeper caught him short of the crease.
The second dismissal was a clear case of pressure resulting in confusion as both Miller and du Plessis ended at the wicket-keeper's end after the former hurried for a run when the latter hit one straight into the hands of Bumrah at short third-man.
"Faf du Plessis is one of the key elements in this side. I know him very well, and the 10 overs that saw him involved with the run-outs before getting out himself will not sit well with him."
Source - Agency