South Africa were well beaten by England at the Oval a week ago in their first match of series, but have since won three games on the trot to all but guarantee themselves a place in the final at Lords next Saturday.
"I think that we've relaxed," Smith said. "Against England at the Oval we were really nervous in both batting and bowling departments and we really didn't play to our potential.
"We've said as a side that we're unbelievable in the nets, but we've just got to start believing in ourselves out in the middle. I think you can see by the way the guys are playing that they are doing just that.
"But we've still got a long way to go in this series. You can win every game and still lose the final so we've really got to be up for what lies ahead for us.
"We can't afford to slack off. We've got to keep building and become a ruthless team that wins a lot more than it loses."
After beating Zimbabwe with a bonus point South Africa now head the table on 17 points, with England on 10 and Zimbabwe nine. It would take a highly improbable series of events for South Africa to be denied a place in the final, but it is not an equation Smith is trying to work out.
"I stay away from the mathematics side of the game," he said. "But all the guys are keen to keep the momentum up and win the majority of our games on this tour.
"We've got some big games ahead and we don't want to let anyone else in the door -- we want to keep them shut out," said Smith.
Zimbabwe captain Heath Streak bemoaned his team's poor display after being asked to bat first, but said his side still believed they could beat England in Bristol on Sunday to give themselves a good chance of making an upset appearance in the final.
"Maybe there is a bit more self-belief that we can beat England and in this series Trent Bridge (where Zimbabwe won by four wickets) gives the guys a lot more inspiration and the knowledge that we are able to compete and beat them."
