With the glorious exception of his 180 in the second Test at Lord's, Root has endured a succession of failures in his first series as a Test opener and his first against Australia.
But he put on 68 with captain Alastair Cook and 50 with Jonathan Trott as England reached 247 for four in response to the tourists' 492.
"You're just so hungry for runs and it's frustrating at times, you have to keep believing in your own game and hopefully it'll turn around at some point," Root told Sky Sports Ashes.
"You go through periods where you score quite freely and then it doesn't come as easy, you have to keep working at your game.
"It's Test cricket as well, blokes will bowl well and you've got to work hard to combat it."
The Yorkshireman's eventual dismissal came when he top-edged a sweep into the grateful hands of Shane Watson and he admitted his frustration.
"I was trying to get the hard sweep away, maybe get four or, if not, one," he said.
"It was disappointing, having done a lot of the hard work and got a good partnership together. It's disappointing from the team viewpoint more than anything."
Root's strike rate of just under 37 was bettered - just - by Kevin Pietersen as he made 50 but was in excess of any other England batsman in the innings thus far on an attritional day.
Root said: "You have to give a bit of credit to Australia, they bowled well at us.
"(The pitch) was quite slow, it's hard to time. You've got to be patient, we need to carry on tomorrow as we finished tonight."
Ian Bell will resume on 29 with Test debutant Chris Woakes on 15.