Anderson was at his unplayable best with the pink ball in Australia's second innings in the day-night test in Adelaide and took 5-43 to bowl the hosts out for 138 and give his side an outside chance of squaring the series.
"When he's able to swing the ball like that, he's extremely hard work and he's very, very damaging," Bancroft told reporters in Perth on Monday ahead of what could be the series-clinching match for the hosts.
"No matter what's going on, it's bloody hard work when the ball is swinging like that.
"You can have the best game plan in the world but there can be a ball with your name on it."
Bancroft added that the pressure Anderson applied in the twilight on the third day of the second test had stymied the normally free-flowing Australian batsmen and made them work for every run.
Anderson's performance, his first five-wicket haul in Australia, turned out be in vain in the end, though, as the hosts steadily chipped away at England on the fourth day when they were chasing 354 for victory.
Josh Hazlewood then took two quick wickets early on the fifth day before Mitchell Starc ripped through the tail to bowl England out for 233 and give Australia a 120-run victory and 2-0 series lead heading to the WACA for the Dec. 14-18 match.
Perth local Bancroft was looking forward to playing on his home ground, having scored a career-best 228 not out there against South Australia before he was called into the national side to make his debut in the first test in Brisbane.
While the WACA pitch had flattened and become more batsmen friendly compared to the past when it provided steepling bounce and express pace, Bancroft said it would still give the swing bowlers like Anderson some assistance early on.
"Always in the first session at the WACA it can be quite hard work, but like anything, if you're willing to put in the hard yards early you can reap rewards later in the game," said Bancroft.
"It's such a fast outfield that you don't have to worry too much about scoring, the ball goes through the infield and you instantly get two even if you don't hit it really well.
"That's the beauty of playing at the WACA."
(Writing by Greg Stutchbury in Wellington; Editing by Nick Mulvenney)
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