Several cricket pundits argued that Wade was guilty of obstructing the field, with social media inevitably erupting after the incident.
Australian Test opener Usman Khawaja tweeted: "Can't believe they didn't appeal."
Law 37.3.1 states: "If the delivery is not a No ball, the striker is out Obstructing the field if wilful obstruction or distraction by either batter prevents the striker being out Caught."
At the post-match presentation, Buttler confirmed that he withdrew the team's appeal against Wade, giving the Australian an extra life at the crease.
"They said, 'Did we want to appeal?' and I said, 'No'," he explained.
"I just had my eyes on the ball the whole time, so didn't really see what happened.
"We've only just got to Australia so I thought, let's carry on in the game.
"I didn't see it live, I was just looking at the ball … I don't know what I'm appealing for really.
"I could have asked maybe some of the other boys to see if they had a better view but I just thought, get on with the game."
Asked if he would have done the same in a World Cup match, Buttler replied with a smile: "Maybe."
Wade, who was on zero when the incident occurred, was eventually dismissed by England seamer Sam Curran in the final over for 21 (15) as the visitors clinched an eight-run victory.
Australian all-rounder Marcus Stoinis defended his teammate after the match, telling reporters in the post-match press conference: "There's a lot that goes on there when you get hit in the head and you're running around.
"You don't know where the ball is … it is chaos."
Buttler's generous act was undoubtedly the most diplomatic approach, but English cricket fans quickly pointed out the Australians weren't as charitable when confronted with a similar scenario seven years ago.
In 2015, England all-rounder Ben Stokes was given out obstructing the field during an ODI at Lord's after blocking a throw at the stumps from bowler Mitchell Starc.
Wade, wearing the gloves behind the stumps, appealed for a wicket and Australian captain Steve Smith opted not to withdraw the appeal.
"Wadey had a good view of it behind the stumps," Smith said at the time.
"He said straight away that he thought the ball was missing Stokesy and it was going to hit the stumps.