The tourists are 9-232 in their second innings, just 40 runs ahead with one day left to play in Chennai.
Henriques has performed superbly with the bat during the match, backing up a first innings 68 with a defiant 75 not out.
And a gritty 57-run stand between the debutant and Nathan Lyon (eight not out) for the final wicket has given Australia a glimmer of hope in their bid to avoid defeat.
"We haven't lost this Test yet," Henriques told reporters after the day's play.
"There's certainly a lot of hope and from my point of view, you just don't know what can happen.
"Obviously the odds are stacked against us at the moment. We go into tomorrow being the underdog and whether it's rain, whatever it is ... you just never know.
"Whatever we get tomorrow will have to be enough (to set India a target). If Nathan can keep batting like he did tonight ... I thought he did a fantastic job.
"Hopefully I can squeeze a few more (runs) out tomorrow and (a lead of) 100, 150, 200 ... we won't be setting targets. We'll just be batting as well as we can."
Henriques conceded the worn Chennai batting strip was providing plenty of problems for batsmen but the all-rounder is determined to keep Australia's slim lead ticking over.
"It's a very tough wicket to start on," he said.
"I had a couple of balls hit my glove early on in the innings. It did get a little bit easier the more time you spent out there but the ball does misbehave out of the rough. It is quite abrasive and there are some balls that are jumping.
"Hopefully (I) go out there tomorrow and keep contributing and (we) post something that can be defendable. And hopefully (we) give Nathan Lyon a chance to bowl on a day five wicket here."
India all-rounder Ravindra Jadeja, who has figures of 2-68 from 26 overs, said the Australians' desire to play aggressively may have been their downfall in the second innings.
"Australian (s) have this ego ... they try to play more positive," Jadeja said.
"If they have played three (or) four overs (of) maidens, they show aggression so they don't come under pressure.
"But this wicket has been turning through the match and we've bowled well ... everyone has played his role."
Jadeja rejected suggestions the pitch was overly friendly to spin bowlers and said their plan was simple on day five.
"We've got to take their last wicket quickly and the runs that are left to score, 50, 55 or whatever, get them," he said.
