The duo picked up all 10 England wickets in the first 90 minutes of play before New Zealand captain Kane Williamson guided the hosts to 175-3 for a lead of 117 runs at stumps.
"We certainly did not bat very well this morning. They bowled extremely well but we batted extremely poorly," Bayliss said.
"I think it must have been a mental thing, our feet looked like they had lead in them. We didn't make too many right decisions with our footwork.
"We got caught behind the crease to fairly full balls, which allows the ball to swing and then we were nowhere. It looked a little bit like we were rabbits in the headlights."
Williamson had earlier won the toss and opted to bowl with the pink ball in the first day-night test in New Zealand, but Bayliss said the conditions had little to do with the visitors' capitulation.
"There were good conditions this morning. A bit of green grass on the wicket but nothing out of the ordinary that you would not expect for the first day of a test," Bayliss added.
"Today we were off it - not just a little bit, but a long way and we were not good enough."
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
