Root continued his problem of not converting half-centuries into three-figures when he fell for 67 early on the final day in Adelaide - having played brilliantly to see out the fourth evening under lights - to all but end England's hopes of chasing down 354 to level the Ashes series.
In the second innings of the first Test, he was lbw the ball after reaching his half-century when England were trying to form a lead to challenge Australia in what ultimately became a 10-wicket defeat.
"It's a monkey on his back and it will continue to grow with so many fifties not being hundreds," Swann told ESPNcricinfo. "I'm still convinced it's because he's had the captaincy put on him. I wish they hadn't, I wish he didn't have the burden and could just be our best-ever batsman but that decision has been made and this tour will be tough on him because that pressure will build and build."
Since becoming captain, Root has passed fifty in nine of his 16 innings but has converted just two into centuries - 190 at Lord's in his first knock as captain and 136 against West Indies at Edgbaston.
However, his poor conversion rate - which is significantly lower than the likes of Steven Smith, Kane Williamson and Virat Kohli - has not just become an issue with the leadership. At the end of 2014, Root had five centuries and eight fifties but since then has made 27 fifties and only eight centuries.
"In big series your senior players have to step up and lead from the front," Root said after the defeat in Adelaide. "I tried to do that on the fourth evening. Unfortunately, I could not carry that on and that is really disappointing. I've been concerned about not converting my fifties into hundreds for a long time now. It hurts me personally a lot."
However, Root is not the only batsman England need more from. In four innings during this series their top score is James Vince's 83 and there have been just five half-centuries. Australia, meanwhile, have had two match-defining centuries by Smith and Shaun Marsh.
"The top six just aren't churning out the scores you need to win Test cricket," Swann said. "Vince got a brilliant 80 in Brisbane but since then hasn't performed, Mark Stoneman is looking good but not converting the starts and the big guns Cook and Root just aren't scoring hundreds. There are problems. The scoreboard has to read 400-450 if you want to win here."
Further down the middle order there are vulnerabilities as well with Moeen Ali's promotion to No. 6 to replace the absent Ben Stokes yet to bring significant returns. Moeen has also struggled for impact with the ball, comfortably being outbowled by Nathan Lyon, but it is so far a small blip in a very successful year for Moeen and Swann wants him to believe in his own ability.
"One person I wouldn't drop despite very ordinary performances is Moeen Ali. You need to still play a spinner at Perth and it would be a very big call to bring in Mason Crane at probably the least spin-friendly ground in world cricket. But Moeen has to start believing in himself as a bowler. If he's injured he has a week to get over that and he has to bat with conviction and flair. When he's on fire he's a dangerous prospect but at the moment he's 50% Moeen."