"When we went out so early the country took it badly," Smith admitted Tuesday, ahead of the series where Zimbabwe also feature.
"We realise we owe the South African public something big," added Smith, 22, who only came into the Proteas' World Cup squad after an injury to Jonty Rhodes.
Following the World Cup debacle left-hand batsman Smith lept from stand-in to skipper, replacing all-rounder Shaun Pollock.
But while Pollock remains a key member of the side, other stars have departed the scene.
Fielding maestro Rhodes, now playing for English county Gloucestershire, and fast bowler Allan Donald have both retired from international cricket.
Controversially, Lance Klusener, 31, was left out of the squads for both the triangular tournament and the subsequent five Test series in England, even though the all-rounder was available.
Much will depend on the peformances of Pollock and new-ball partner Makhaya Ntini.
There was a huge gap in class between the pair and the rest of the South Africa quicks at the World Cup where spinner Nicky Boje was repeatedly targeted.
Smith, sounding like an old-fashioned English county professional, said Pollock-like discipline represented South Africa's best way back to bowling respectability.
"We want to become a really tight unit that gives nothing away, that builds extreme pressure with dot ball after dot ball."
But in order to help build that pressure the batsmen will have to give the bowlers defensible targets and runs will be expected from the gifted Herschelle Gibbs as well as Smith himself.
England, like South Africa in a post-World Cup rebuilding phase, go into the series boosted by a 2-1 one-day triumph against Pakistan concluded Sunday.
Under new one-day skipper Michael Vaughan, England are a rejuvenated fielding outfit, with fast bowler James Anderson the jewel in the crown of an improving attack.
But doubts remain about the solidity of their batting.
Vaughan said Tuesday that "South Africa are the second-best one-day team in the world," a remark unlikely to either deflate home hopes of victory or soften up Smith's men.
Although Zimbabwe had the best World Cup of any of the triangular sides, reaching the Super Six second phase, they have had a miserable tour of England so far.
Zimbabwe, minus leading batsman Andy Flower, were thrashed by an innings in both Tests and also suffered an embarrassing one-day defeat against Ireland.
But in all-rounders Andy Blignaut and Sean Ervine, Zimbabwe do have potential one-day match-winners.
England and Zimbabwe get the series underway at Trent Bridge on Thursday with South Africa entering, against England, at The Oval on Saturday.
June 26: England v Zimbabwe, Trent Bridge
June 28: England v South Africa, The Oval
June 29: Zimbabwe v South Africa, Canterbury
July 1: England v Zimbabwe, Headingley
July 3: England v South Africa, Old Trafford (day/night)
July 5: Zimbabwe v South Africa, Cardiff
July 6: England v Zimbabwe, Bristol
July 8: England v South Africa, Edgbaston (day/night)
July 10: Zimbabwe v South Africa, Rose Bowl
July 12: Final, Lord's