Bowled out for 195, the Black Caps fought back to dismiss the South Africans for 108.
After the match New Zealand captain was able to reflect on his defiant innings of 89 which held his side together, while his counterpart could only fume at the pitch.
"It's always tough to sit and moan about a wicket when you've lost, but in terms of an international tournament I don't think the wicket was of a good standard today," said Smith, South Africa's top scorer with 42.
"The pitch deteriorated as the day went along. Batting second was very, very difficult. All credit to Stephen. His knock held their innings together and without him, who knows, we might have been chasing 120-130.
"The pitch broke up, the ball turned a hell of a lot. I don't think the pitches are going to provide an 100 overs of good cricket."
Man of the match Fleming said he was expecting the wicket to deteriorate.
"We went with what we saw, which was a very dry wicket, and as it turned out it got worse," he said.
"The pitches are a bit different this time around in India. As the tournament progress, it is going to be tough on the viewers and in this respect I can understand Graeme's complaints.
New Zealand celebrate their
"But our job is to play on whatever pitches are given to us and play accordingly.
"We were aiming 220 to 230, which we thought was really competent on this pitch. Once we saw the ball stopping a bit off the wicket, we realized that we are in with a chance in this game," said Fleming.
The left handed captain, who opened the innings, remained resolute as ever as he lost numerous partners, before he was ninth out in the 44th over just as he was closing in on his 10th one day century.
Their next highest run scorer was Brendon McCullum’s 21 was the next highest score as New Zealand battled with the dry surface.
New Zealand seamer Kyle Mills reeked havoc from the opening as he claimed three wickets with his first 19 deliveries to reduce the Africans to 25-3 by the eighth over.
Jacob Oram then tore through the middle-order as the Proteas plunged to 71-6, while off-spinner Jeetan Patel finished with figures of 3-11 from his 3.1 overs.
Meanwhile, veteran South African seamer Shaun Pollock became the fifth bowler to claim 350 one-day wickets when he bowled Lou Vincent for 17 to end an opening stand of 27.
Pollock, 33, joined the rare club led by Pakistani Wasim Akram (502 wickets) and followed by Muttiah Muralitharan of Sri Lanka (419), Waqar Younis of Pakistan (416) and Sri Lankan Chaminda Vaas (358).
New Zealand next play Sri Lanka on Friday. South Africa take on the Sri Lankans in Ahmedabad on October 24.