The Proteas were undone by an England side that produced one of its very best displays in this format as South Africa lost after starting the second round Super Eights with a 13-run victory over New Zealand.
Such are the permutations in Group E that even a win over Pakistan in St Lucia on Monday might not be enough for South Africa to go through to the semi-finals.
But Smith is determined the Proteas give themselves every chance.
"How we bounce back is going to be crucial, Pakistan on Monday is obviously an important game for us," Smith said. "Bouncing back and putting in a good performance on Monday is obviously a challenge."
Fast bowlers Dale Steyn and Morne Morkel conceded a huge 90 runs in eight overs between them as England's South Africa born second-wicket partnership of Kevin Pietersen, man-of-the-match for his 53, and Craig Kieswetter (41) helped their adopted country to a total of 168 for seven.
What made it worse for South Africa was that Morkel had Kieswetter 'caught' off a no-ball for seven.
It was the second time this tournament that over-stepping had cost Morkel a wicket after Suresh Raina made a century in India's first victory against South Africa, having been given a reprieve by a no-ball when on five. "I think the first six overs was especially disappointing," said Smith. "Basic mistakes, no balls, missed chances up-front proved costly for us. "We really could have had England three or four down in those first six overs but basic mistakes from us allowed them to get a partnership that has proven to be the difference between the two sides."
Turning to Morkel's no-ball problems, Smith added: "It is very frustrating. It seems to come and go, he goes through phases where he doesn't bowl them and then he goes through phases when he does - I guess it's up to the bowling coach (Vincent Barnes) and Morne to put it right."
One consolation for South Africa was the form of off-spinner Johan Botha.
Opening the attack, Botha took a miserly two wickets for 15 runs from his four overs.
"I thought he bowled really well, we used him up-front against the openers, we thought maybe a change of pace up-front might work and it did," Smith said.
"Under pressure, going at tens, he was really controlled for us."
But England spinners Graeme Swann and Michael Yardy then took five wickets between them as South Africa suffered a top order collapse that effectively ended their hopes of a successful run chase.
"They bowled well, they knew after us not getting a really powerful start that we were going to have to try and attack them... We played right into their hands so it was kind of a snowball effect really," Smith explained.
But it was the dynamic Pietersen, well supported by Kieswetter, which put South Africa on the backfoot.
Smith has had an often fraught relationship with Pietersen, arising from the now England batsman's comments that he left South Africa because a racial quota system favouring non-white players was hampering his progress.
However, the South Africa captain had no doubt about the quality of Pietersen's latest display.
"When he plays like that you have got to be on the top of your game and you can't afford to miss chances, as we did.
"But when he is on song like that he is a difficult guy to bowl at."
Pietersen's major ally was Kieswetter, a former South Africa Under-19 international who has decided to pursue a senior career with England - a move that has led to plenty of comment in both countries.
But Smith, asked if he felt it was "galling" to see Pietersen and Kieswetter scoring runs for England, rather than South Africa, replied: "No, not at all. Come on guys, let's keep it real."
Copyright AFP (Agence France-Presse), 2010