England lost their last five wickets for six runs to be bowled out for 179, leaving Australia chasing 231 for a victory which would put them 4-0 up in the series.
They had already knocked off 30 of those runs without loss by the close of play as Australia reasserted their authority.
"After the start we got it's disappointing to be ending the day in the field," Bairstow told Sky Sports 2.
Asked why England continue to suffer batting collapses during this series, he added: "To be honest I don't know. If we knew that, we'd have put our fingers on it and moved on. Obviously it's disappointing but I'm sure tomorrow we can go out and take those 10 wickets like we did in the first innings."
Bairstow, who replaced Matt Prior in the England team for this Test, insisted he was enjoying the experience despite being thrown in at the deep end against the likes of the in-form Mitchell Johnson.
"It's a fantastic experience," he said. "That's the nature of sport, that's why you practice day-in, day-out, to try to come out and play."
He began his own innings positively, hitting two sixes off Nathan Lyons who was himself on his way to five wickets, before edging behind to become Johnson's 30th victim of the series.
"I guess that's the way I play," Bairstow said. "You seen me for a few years now and that's how I like to play my cricket. I was pleased to get off to a decent start so I'm disappointed I didn't go on."
Australia will start day four needing a further 201 to win, but Bairstow remains confident it can be England celebrating.
The hosts were dismissed for 204 in the first innings and a repeat will see the tourists get off the mark.
"Of course we can do it," he said. "In the first innings we bowled them out for less than they're having to chase. The patience our bowlers showed, and the skill in getting the ball moving sideways, it was a fantastic showing from our bowlers and if we can get it going sideways again we know how dangerous our bowlers can be."