England went 2-0 down in the series after falling to a 120-run defeat in the second Test in Adelaide as Australia took six wickets in the first session of day five.
England had resumed on 176-4 with hopes of a chasing down their victory target of 354 after fighting back on days three and four.
But they were soon ripped away as captain Root and Chris Woakes were dismissed without adding to their overnight total.
“Last night and leading into that we showed what we can do and we showed the side that we actually are,” said Yorkshire’s Root. “We need to make sure we repeat those performances for longer periods of time. We came to the ground this morning well in the fight but unfortunately those two early wickets really did cost us.
“If we got in and went on and make a decent partnership there it is a completely different game. But, unfortunately, we just weren’t able to do that.
“It’s very frustrating, I thought the way we responded in the second innings with the ball and then the fight and resolve we showed last night with the bat was outstanding.
“It would have been nice to be two or three down going into today, but, credit where credit’s due, they bowled very well up front and we just have to be better.”
Root won the toss and opted to bowl, but his bowlers wasted helpful conditions as Australia were allowed to post a commanding first-innings total. Given the chance again, though, Root insisted he would still make the same call.
“There are lots of things that you look back on and maybe do differently but that wasn’t one of them,” he added.
“I don’t actually (regret it), you want to give your bowlers the best chance to take 10 wickets and in those conditions with the quality that we have I fully expected those guys to take 10 wickets.
“With the rain around and losing some time potentially hampered us, we would have had 10 overs with the second new ball that night that were taken away from us under lights.”