The Scorchers last night fell by three runs to the Thunder at Spotless Stadium, after the home side won the toss and tallied 4-175.
Perth stumbled to 4-35 in its chase, but recovered through Bancroft (75 not out off 56) and Hilton Cartwright (65 not out off 41) to come within a boundary of victory.
It was the third time this season the Scorchers had tallied a total of 170 or more and came off the back of a 137 not out record partnership for the fifth wicket for the Club between Bancroft and Cartwright.
Bancroft said the defeat was disappointing, but that the silver lining was the side defying the odds to post big scores.
"It was very disappointing and we just couldn't get enough big overs in," Bancroft said of his and Cartwright's chase.
"I suppose to get as close as we did, with the wickets we lost early, is a good thing, but it's disappointing.
"At the end of the day, we didn't win the game, so I feel that I left the job undone out there.
"It's really positive (that we're scoring 170 or more consistently) and two of our (strongest batters) - the Marsh brothers - aren't playing, either, so it's good to see other players step up.
"It was a good wicket (at Spotless Stadium) and we were able to be really competitive and chase a good score down.
"So, I think that side of our game is really growing with confidence.
"Ideally, we'd like to keep teams down to as low a total as possible, but knowing that we can go out and chase a big 170, 180 score is really positive for us."
The Scorchers have been impacted by injury and national call-ups, with more than half the starting XI unavailable, but remain in second position on the KFC Big Bash League table.
The exit of competition leading wicket taker Andrew Tye, Jhye Richardson and David Willey to international duties prior to last night's game, combined with injuries to Jason Behrendorff and Nathan Coulter-Nile, rocked the Scorchers' bowling stocks.
However, incoming Englishman Tim Bresnan captured two wickets against the Thunder, while debutante Matt Kelly took one on debut and the crucial catch of Shane Watson.
"I think the players we had come in today are very capable of doing the job that the other two guys are able to do," Bancroft said.
"Matt Kelly on debut was fantastic and he really showed under pressure that he was able to stick to his change-ups and back himself.
"Tim Bresnan will obviously get better; he's just hopped off a plane and he's a class player.
"Everyone we have faith in, but across all areas we just weren't good enough.
"It was close, but we let ourselves down a bit."