Australia lead the series 2-0 and will regain the Ashes if they win at the Waca, where England last won in 1978.
“In the face of adversity, people want to see you put in big performances and prove why you have been chosen to play for England,” said Root.
“If we get that right there is no reason why it can’t be 2-1 this time next week.”
At the weekend, batsman Ben Duckett was dropped from an England tour game and then suspended for the remaining fixtures on the England Lions tour for pouring a drink over James Anderson in a Perth bar.
That followed all-rounder Ben Stokes being arrested in September for his part in an altercation outside a Bristol nightclub and Jonny Bairstow being accused of ‘headbutting’ Australia’s Cameron Bancroft.
“It’s frustrating that in the obvious circumstances and position we’re in guys have made silly mistakes that are going to get blown out of proportion,” said Root.
“It’s not a fair reflection on this group of players. They are good blokes, good people, but incidents like that let us down and lead people to believe otherwise.”
Root, 26, is on his first tour as captain after being appointed at the beginning of the year.
He led England to series wins against South Africa and West Indies in the home summer, but the defence of the Ashes has been blighted by the off-field controversy.
“I’m fed up of talking about stuff that’s not cricket,” said the Yorkshire batsman, who joked that he does not know how he still has all his hair.
“I can completely see how captaincy can take its toll. I feel like I’ve learned a large amount. From that you gain knowledge and hopefully that will stand me in good stead moving forward.”
England were beaten 5-0 on their last tour of Australia, a trip that saw Jonathan Trott return home after the first Test, Graeme Swann retire and, in the aftermath, coach Andy Flower resign and batsman Kevin Pietersen discarded.
With England already 2-0 down this time and having to deal with non-cricketing matters, Root said he could understand if supporters were losing patience.
“We’ve got to make sure that we get it right on the field and, for the rest of the trip, that people are talking about us in the right way,” he added.
“It’s about winning. That’s what is going to get people back on side.”
Following the defeat in the second Test in Adelaide, coach Trevor Bayliss highlighted batting as England’s biggest area of concern.
The tourists’ highest total is 302 and their best individual score is James Vince’s 83.
Root is the only player in the current squad to have made a century in the previous 12 Ashes Tests, but has no plans to move from his current batting position of number four.
“It can be perceived as a selfish thing, batting at four, but the way I look at it is the opposite,” he said.
“In my opinion, and in the best interests of the team, four is where I feel it fits best for this group, where I’m going to get the most out of myself.
“If I was batting at three and not producing the runs I would want, it would be ‘are you thinking about dropping down to four?'”
England must end their 39-year winless record in Perth, in the final Ashes Test at the Waca, if they are going to hold on to the urn past Christmas.
Traditionally hard, fast and bouncy, the Perth pitch has been slower in recent years, so uncapped leg-spinner Mason Crane could come into contention for England.
The tourists have opted against promoting pace bowler Mark Wood from the Lions squad yet, though he could be called up later in the tour.
“It’s exciting to be playing in such a historic Test match,” said Root.
“It’s very important that we don’t look too much into the past because there’s already chat that it’s a very different wicket to a typical Waca pitch.
“I’m sure that it will have pace and bounce, but it would not surprise me if it does spin. We’ll have a better indication of that over the course of the next couple of days.
“Ultimately we have to really smart in how we prepare. If we do that and have clear ways of how we go about things, that’s what will give us the best chance of winning, not looking at history and what’s gone before.” (Courtesy BBC)