It came after the Victorian all-rounder snared 3-10 off two overs in a clear Man of the Match effort.
There had been a clear-cut opportunity to remove Maxwell on 40 when Alex Hales put him down in the deep and, expanding on his views later, Morgan added: "It's two dropped catches officially".
"We haven't had much success in T20 cricket for a while now - our rating reflects that - so it was so imperative for this young group, this young exciting group to take us forward and win some games".
Whatever their thoughts about the catch, England had been wasteful in slipping from 1 for 60 after six overs to only 9 for 155, restricted largely by the spin bowling of Maxwell and Ashton Agar, plus the slower-ball variations of Kane Richardson and AJ Tye.
It was a trickier scenario against the Poms though, who had the ball swinging and Australia in trouble at 2-4 in the first over. Maxwell's contribution was his second in as many matches, following a summer in which he had spent far more time outside the Australian set-up than in it.
England squad: Eoin Morgan (c), Sam Billings, Jos Buttler, Sam Curran, Tom Curran, Liam Dawson, Alex Hales, Chris Jordan, Dawid Malan, Liam Plunkett, Adil Rashid, Jason Roy, Ben Stokes, James Vince, David Willey, Mark Wood.
These early incisions gave England a chance, but Short and Maxwell were not unduly concerned by the required run rate and so were able to play with relative comfort in their distinctive styles.
Fresh from his stint with the Hobart Hurricanes, D'Arcy Short was right at home at Blundstone, belting a quick-fire 30 off 20 balls, with two fours and two enormous sixes.
Earlier England was strangled by Australia's spinners. It was comfortable enough for Maxwell to monopolise the strike at the end and so go onto his second T20I hundred. Australia clinched a victory against New Zealand in the first T20I by 7 wickets in a rain-affected match.
The lanky left-armer snaffled a leading edge from the risky Alex Hales but had to run behind Malan at the non-strikers end.
Malan was caught on the rope by Andrew Tye for Maxwell's second, and David Willey (3) danced down the track next ball to give Alex Carey his first worldwide stumping.
David Willey was stumped on the slog for three off Maxwell (3/10), a ball after Malan had been caught in the deep, as England lost seven for 43 once captain Eoin Morgan (22) became Maxwell's first victim.
In typical fashion, Maxwell endured a roller-coaster innings marked by a contentious decision, when he was on 59, after Jason Roy claimed a catch at long-off.