They conceded 592 in just 107.4 overs as England looked to force a result before rain wiped out the majority of the fourth and the entirety of the fifth day. Moody, who played 84 times for his country and has enjoyed an extensive coaching career, believes that Australia must pick Murphy, the 22-year-old offspinner, to restore balance to their attack.
"I know that they would've had their various reasons behind not playing Murphy, whether that was based around the fact that there was the weather that was potentially on the horizon, but that's no guarantee," Moody told ESPNcricinfo. "That would have looked pretty stupid if it had backfired.
"To me, the attack did look like it lacked balance. Murphy is an exciting young bowler. He is not Nathan Lyon, but Nathan Lyon is not Shane Warne either. Murphy needs to create his own path and have his own journey; he has started that already and he has started pretty successfully.
"I'd be surprised if he doesn't come into the side just to create that balance, but also give the team better combinations for Pat Cummins to lean towards. In that fourth Test match, it was almost like he was looking around the field for options - and he was nearly looking in the mirror all the time."
"There's no question Cameron Green has got remarkable upside, but the here-and-now selection is Mitch Marsh"
He suggested that Australia should leave Green out of their side in order to fit Murphy in. "I think playing the two allrounders is a luxury, and to me, at this stage, Mitch Marsh is the one that looks like he can influence the game, which he's already done since he's returned with confidence.
"There's no question Cameron Green has got remarkable upside, but the here-and-now selection is Mitch Marsh. There are very few players in the history of the game that haven't had setbacks, or been left out of sides for team combinations or form or whatever it might be. If anything, it's probably something that might do him [Green] the world of good."
And Moody believes that winning an away Ashes series for the first time since 2001 by avoiding defeat at The Oval would be "a huge achievement" for Australia. "The way that England have been playing Test cricket has been nothing short of outstanding to watch. They have set new standards, which is something to be admired and respected.
"So to get a stranglehold so early in the series was credit to Pat Cummins and his team. To win away from home is difficult anywhere in the world, but probably the two hardest places are India and England. After the way the game petered out at Old Trafford, I would imagine their mindset would be making sure that they put the final nail in the coffin and try to win 3-1."
Moody was speaking at Lord's as Desert Vipers - the ILT20 franchise for whom he works as director of cricket - launched a sustainability initiative which included a full-scale audit into their carbon footprint during the league's inaugural season in the UAE earlier this year.
Vipers called on other T20 franchises to follow suit in order to mitigate the negative impact that short-form leagues have on the environment, particularly with regard to long-haul flights. "Hopefully Desert Vipers have a unique opportunity to be trailblazers for other sporting teams," Moody said.
"When you see significant events happen globally around the impact of heat or flood, that's when it's an eye-opener. Missing a day's play because it's wet is insignificant compared to seeing whole communities impacted by devastating floods, for example, which we're seeing constantly both in Australia and globally."
Matt Roller is an assistant editor at ESPNcricinfo. @mroller98