Snyman (shoulder) and Muller du Plessis (back strain) were ruled out of action on Sunday, while Zain Davids missed the final match with a hamstring injury.
Snyman praised the team’s guts and determination to win the bronze final.
“We started that match with only ten players and played until the very last second of the match, something I am very proud of,” said Snyman.
“Having conceded late tries against them last night and against Fiji earlier on Sunday in the Cup semi-final, the guys proved their determination not to do so again.”
Powell was equally pleased: “We finished sixth in Dubai where we played poorly in our first four matches. We started picking up some momentum and I think we improved further this weekend.
“We let ourselves down at times, but we certainly finished in a much better state than last weekend. This is a good, positive way to finish the second leg of the series, with some momentum to take into the next leg in Hamilton in late January,” said Powell.
Blitzbok winger Siviwe Soyizwapi, agreed with Powell and said it was a “much better feeling” than last weekend.
“We were competitive all along and had we play one of two moments better, we could have been smiling now,” said Soyizwapi.
“Six guys played here in Cape Town for the first time and they would have benefitted from this as well. As usual the crowd came out in massive numbers and it was an honour to play here.”The third place in Cape Town also moved the team up the HSBC World Rugby Sevens Series standings and they will travel to New Zealand in fifth place overall, where they were drawn in the same pool as Scotland, France and Kenya.
The current standings are: 1. USA 38 points 2. New Zealand 37 3. Fiji 35 4. England 30 5. South Africa 29
Rosko Specman was named in the tournament Dream Team.
Bronze medal match: South Africa 10 (5) New Zealand 5 (5)
South Africa – Tries: Rosko Specman, Dewald Human.
New Zealand – Try: Sione Molia.
Cup semi-final: South Africa 12 (7) Fiji 17 (12)
South Africa – Tries: Siviwe Soyizwapi, Rosko Specman. Conversion: Justin Geduld.
Fiji – Tries: Vilimoni Botitu, Waisea Nacuqu, Alosio Naduva. Conversion: Nacuqu.
Cup quarter-final: South Africa 21 (7) Scotland 12 (7)
South Africa – Tries: Justin Geduld, Rosko Specman, Werner Kok. Conversions: Justin Geduld (3).
Scotland – Tries: Sam Pecqueur (2). Conversion: Gavin Lowe.