With less than a minute left, Gawn's miscued kick after a mark in the back pocket went straight to Collingwood's Will Hoskin-Elliott to confirm the result, with the Magpies winning 11.6 (72) to 10.11 (71) on Monday at the MCG.
May angrily approached Gawn on the final siren. The captain also made his feelings clear before pushing May away.
Teammate Daniel Turner had his arm around Gawn and was trying to settle their hot tempers.
"We just both want to win and I'm not exactly sure what actually happened - it was very loud with the crowd and what-not," Gawn told reporters later.
"But we both want to win and it was a very disappointing last 30 seconds in the way it played out."
Coach Simon Goodwin said Gawn and May soon sorted out their differences.
"Two competitors, frustrated - two leaders (who) have an incredibly strong relationship, obviously disappointed with the outcome," Goodwin said.
"They've moved on pretty quickly - they're in there having a good chat about it."
Gawn said that after he took the mark, he was called to play on and he thought the best option was a big kick out of defence - but he miscued and turned it over.
"I thought it was weird I got called to play on. I don't think I really moved," he said
"And then a ruckman kicking from the back pocket, when he's called to play on, it's not the best recipe for us to try and win, so I thought a chaos ball was our best option.
"Maysy just wants to win and he holds us all to high standards.Â
"It was too loud for me to even properly say what was said."
Collingwood led by 20 points in the third quarter, but fell behind early in the last term, before Dan McStay kicked the final goal.
Both sides had further chances to score, but Gawn's snap at a boundary throw-in narrowly missed and a set shot by Koltyn Tholstrup didn't quite make the distance as the Demons fell agonisingly short.
Almost a year to the day since last season's injury nightmare, Demons star Christian Petracca returned to the same stage with 26 disposals and five clearances.
But it was some of Collingwood's stars who shone brightest as the ladder leaders made it five wins on the bounce and improved their record to 11-2 ahead of a mid-season bye.
Jeremy Howe (26 disposals) was brilliant in defence, Josh Daicos (34) stood up in the middle and McStay kicked two important goals.
Nick Daicos kicked one goal from 19 disposals as he struggled with a tight tag from rebadged Melbourne winger Ed Langdon.
The Demons (5-8) had their chances as Bayley Fritsch and Kysaiah Pickett kicked three goals each.
Pickett put Melbourne in front briefly in the final quarter and Clayton Oliver (30 disposals, nine clearances) worked hard.
The Demons dominated centre clearances (16-7) and overall clearances (39-29), and had a 54-45 advantage in forward entries, but couldn't make it count.
Langdon wore Daicos like a glove from the outset and their tussle was central to multiple spotfires throughout a tight first half.
Two Pickett goals bookended three straight Collingwood majors in the second quarter, his first a fortuitous hack off the deck from 45 metres.
But the Demons managed just 2.4 for the term - to Collingwood's 4.0 - despite dominating the inside-50 count (21-9).
The Magpies, who enjoyed an 18-11 advantage in free kicks in the first half, led by eight points at the main break after Tim Membrey slotted a set shot on the siren.
Collingwood's victory extended their recent dominance of Melbourne to 11 wins in 13 meetings.
9°C