Ben Stokes' inspired display kept the five-Test series alive as hosts England amassed their highest ever fourth-innings run chase in Leeds, where the hosts prevailed by one wicket last week.
Australia, however, will be able to welcome talisman Steve Smith back to the fold for the Old Trafford Test after the star batsman missed the Headingley clash due to a concussion sustained at Lord's.
Smith will play a three-day tour match against Derbyshire, with Khawaja captaining an Australia side which also includes Marcus Harris, Cameron Bancroft and Marnus Labuschagne.
Khawaja acknowledged Australia's defeat was a tough blow to take, but he has no doubt the tourists will bounce back before the end of the series, with one win from the two remaining Tests enough to retain the urn.
"Disappointing for us but hopefully it'll make the next game or the game after even more sweet when we do win," Khawaja said. "It was an excellent innings [from Stokes]. The way it ended, the drama, you couldn't write a script like that. It was heartbreaking for us as a team.
Test cricket at its most dramatic! Hats off to Ben Stokes and @englandcricket on an amazing performance to level the series at 1-1.
— Cricket Australia (@CricketAus) August 25, 2019
"It was a good game if you look at it from the eyes of a fan, what an amazing game. I hope it's not too much of an epic [series]. The last game was clearly epic for England fans, and there have been great Ashes rivalries and games.
"We played beautifully in the last game, we were so close to winning the Ashes, and if a few things go our way at the end then we would have done.
"We've played some really good cricket and we're confident we'll get that win."
With the fourth Test not starting until September 4, there is a 10-day gap between the matches, though Khawaja does not believe it will have been easier for Australia if the break was a shorter one.
"It doesn't make much difference. We already had two Tests back-to-back so it was pretty tough," Khawaja said.
"It's nice to get a bit of a break, refresh and go for the next two. Test cricket's always hard work, always tough competition. There's a lot of depth with Australia's squad, and they all deserve to play which is a good thing."
Photo Getty Images. Caption: Usman Khawaja in action at Headingley