In just his third game since crossing from the Western Bulldogs, Everitt came back from a horror start on Eagle forward Quinten Lynch to kick two crucial goals as the Swans' clawed back a 12-point deficit heading into time-on of the last quarter to win a thriller.
His first goal put the Swans back in front and another after the siren secured the victory.
But it was the fact he was able to recover from the beating he took from Lynch - who kicked four first-half goals - that really impressed his new coach.
"He has played the whole pre-season and first couple of rounds down back and we knew he could go forward, but to be honest we didn’t expect him to kick those goals in the last quarter," Longmire said.
"We lost Sam Reid in that third quarter, so we needed a tall forward and he really filled that bill. When he went forward he was really important in that last quarter and gave us a real target. He's a very good kick, too."
Longmire has witnessed the tremendous fighting spirit the Swans possess over a decade at the club and he said that spirit was beginning to rub off on some of the club's young players.
"Fortunately this group over a long period of time has been known for having a go for four quarters. That's been the most pleasing and for a number of years now, even when they look out of the game, they will just find a way," he said.
"Hopefully some of the younger players are learning that as well. Gary Rohan came on and made a real difference, Alex Johnson was good in his first game and that's the sort of thing we need to breed to maintain our pressure for four quarters no matter what the scoreboard is."
Longmire is looking forward to the challenge of taking on Geelong next Saturday night in the club's first home game at the SCG for the season.
Lewis Roberts-Thomson won't return, but Tadhg Kennelly could if he gets through a run for the Sydney Swans reserves team on Sunday.
"The exciting thing for the footy club at the moment is that we get to play Geelong next week at home," he said.
"Hopefully there's plenty of red-and-white people there and we get a big crowd at the SCG against one for the gun teams of the competition.
"[Kennelly] played 75 minutes last week and we hope he gets through the reserves. We need to make sure that our players, with three on the bench, can play 100 minutes and hopefully he pulls up well from the game."
