South Africa, second in the ICC one-day rankings, lost to New Zealand in their opening match on a tricky Brabourne Stadium pitch in Mumbai and another defeat in the four-team group would all but end their hopes of qualifying for the semi-finals.
Sri Lanka must also go for a victory after registering one win and one loss ahead of their concluding pool game.
"We need to grind a little more," Smith told a news conference on Monday, referring to Sri Lanka's ability to apply pressure in the middle overs through their spin trio of Muttiah Muralitharan, Sanath Jayasuriya and Tillakaratne Dilshan.
"Adapting to conditions is crucial to success in this tournament. Whether you bowl first or bat first you've got to be able to adapt to conditions as quickly as possible.
"Adapting to the wicket is the key for us. Hopefully we can put out a good combination tomorrow that wins us the game."
Smith also backed his side's batting strength.
"Our first seven or eight are among the best in the world and we cover all the areas pretty well. It is about getting it right on that day."
Sri Lanka lost their opening match to Pakistan but bounced back quickly with a comprehensive seven-wicket victory over New Zealand.
Off-spinner Muralitharan grabbed four wickets for 23 and left-arm spinner Jayasuriya took 2-26 off his 10 overs against New Zealand after the pacemen had provided early breakthroughs.
"Sri Lanka are probably the form team in the tournament," Smith said.
Sri Lanka won 10 straight one-dayers before losing to Pakistan.
"There's pressure on both of us tomorrow to play well," he said.
Sri Lanka captain Mahela Jayawardene described the clash as a quarter-final.
"We do not want to place our destiny in someone else's hands. It is up to us to get there (the final)," the stylish top-order batsman said.
Jayawardene dismissed notions that South Africa were vulnerable against spin and coach Tom Moody said: "Most of the teams have adjusted their strategies to the sub-continent conditions. The tournament is wide open."
