Waugh said his team faced one of their greatest challenges in years after slipping 1-0 behind with two matches to go.
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"They came back to win the final two Tests in Calcutta and Chennai so there's no reason why we can't do it."
India had not won a test on Australian soil for 22 years and they seemed to have little hope this time when Australia racked up a massive first innings total of 556 thanks to Ricky Ponting's career-best 242.
Rahul Dravid made 233 and Vangipurappu Laxman 148 in India's reply of 523 before Australia lost their grip when they collapsed to 196 all out in the second innings.
India sealed a four-wicket after tea on the final day at Adelaide Oval.
The only other side to win a match after conceding more runs in the first innings was England, also against Australia, in 1894-95.
"If we got 30-40 more runs we could have been in a position to win the match but we probably let ourselves down with our shot selection," Waugh said.
"We were attacking and maybe we should have pulled it back a bit but it's in our nature to try and play for a win."
Australia haven't lose a series at home for a decade.
Waugh, who is retiring after this season, added: "We like to win but it's nice to have a contest. This is a situation that we haven't been in in Australia for the past few years.
"We're under a bit of pressure so it's a great challenge for this side and we're looking forward to the next two Test matches.
"We missed a few half chances but there's not a lot of things we did wrong, India played very well and you have to give them credit for that."