The Proteas have been outplayed in the opening two games, losing by six wickets in Brisbane in a Test that lasted only two days before being swept by an innings and 182 runs in Melbourne.
Although they cannot win the three-match series, the tourists still have faint hopes of reaching the World Test Championship (WTC) final if they beat the hosts and clean-sweep the West Indies in two matches at home starting next month.
"There's plenty to play for," Elgar told the media ahead of the Sydney Test. "We're playing for pride, we're playing for a potential place to the WTC final. So we've also got a lot to play for.
"That's a massive incentive for us and for me you play every Test match like it's your last and hopefully we can put on a better spectacle this time.
"We always want to play good Test cricket and be a thorn in the side of the opposition and we'll be aiming to so better again this time."
The visiting captain was also asked whether he had changed his perception about playing an extra batter instead of a frontline bowler.
The Proteas have gone into both previous Tests with six batters and five bowlers and Elgar said they were leaning towards the same balance instead of playing an extra batter to help a fragile unit.
Elgar added: "I'm still thinking towards 6-5, but all options are on the table for us. To play seven batters would be a massive call for us and a massive ask for our bowling unit to obviously cover those four spots.
"The workload has been pretty hectic on our fast bowlers of late, especially in the last Test where they really pushed quite a few numbers with regard to overs bowled.
"To expect them to come into a Test match and only have four bowlers, potentially only three seamers, is quite a big ask for them."