South Africa claimed Pakistan's last six wickets for 20 runs to win the fifth and deciding one-day international by 14 runs in Lahore on Monday, claiming the series 3-2 to go with their 1-0 triumph in the two-match Test series.
"It was a hugely successful tour and it was really special to win both series," Smith told reporters on the team's return to Johannesburg late on Tuesday night.
"We felt like we achieved something really special because we all realise how tough it is to win on the subcontinent. It was a fantastic feat by this team."
Smith and the team left South Africa the day after the Twenty20 World Cup ended in the country with the players under fire for their early exit from the tournament, battling chilly relations with their own board and facing security concerns in Pakistan.
"We didn't let all the off-field stuff around get into the team environment and it boils down to the maturity and consistency of the squad. And when we got to Pakistan, we were well looked after in terms of the security around the team," Smith said.
New Zealand have already arrived in South Africa for two Tests, three one-day internationals and a Twenty20 match, so there will be little rest for the South Africans.
"We have started the summer very well, but we need to continue in the same vein. We will have to come out firing because we can take nothing for granted against New Zealand," coach Mickey Arthur said.
