England trained five times - once at Allan Border Field, and four times at the Gabba - before the second Test, opting against pink-ball match practice against the Prime Minister's XI in Canberra. They were heavily beaten, losing by eight wickets after four energy-sapping days in the heat, and McCullum suggested that their decision to ramp up their training had backfired.
"Leading into this Test match, I actually felt like we over-prepared, to be honest," McCullum told Australian broadcaster Channel 7. "We had five intense training days. When you're in the heat of the battle, as we all know, sometimes the most important thing is to feel a little bit fresh and make sure your top two inches [of your head] is completely sound.
"I think the boys just need a few days off, and probably need to just change up a few of the training methods a little bit. I'm a horse-racing man, and you wouldn't just keep doing the same thing with your horse, you'd send it around in figure-eights or over the little jumps, just to try and switch it on a bit. We'll look at some alternative methods over the next few days."
England's preparation has been heavily criticised throughout this tour, specifically their decisions to play a single warm-up match against the Lions squad at Lilac Hill, a club ground in Perth, and to turn down the opportunity to play the pink-ball PM's XI fixture between Tests. Stuart Broad described their bowlers as "undercooked", while Michael Vaughan said on Sunday: "No one can tell me that this England management has given this England team the best chance [to win the series]."
The squad and support staff will travel to a coastal resort in Noosa - two hours' drive up the Queensland coast - on Tuesday for a four-night "mid-series break" which McCullum said would provide them with an opportunity to reflect on the first two Tests: "[It] will be good to spend a bit casually and just let the dust settle on what's been a pretty intense couple of weeks and start to plot and plan our way back into the series."
England will then train three times - rather than five - in Adelaide before the third Test starts on December 17.
Ben Stokes, their captain, also defended the Noosa trip, arguing it would be "very, very important" for his players to stay fresh and insulate themselves from the pressures of the tour after an intense start to the series.
"We've been here four weeks, and it's been pretty full-on, on and off the field," Stokes said. "As physical as this game is, a huge part of it is also the mental side of it. I know that. I've experienced that. I know what the game can do to you when things aren't quite feeling right or going well.
"Trust me when I say that it is so, so important that teams… [can] go away as a team and almost put the pressures of this aside for a couple of days, that doesn't mean that everything just disappears, and we don't speak about what's going on. Those conversations are constantly happening.
"This is a high-pressure environment. We chose to do this. We're lucky enough to do this. It comes with the job, but it's also very, very important that when you do get the opportunity that you are able to go away and refresh your mind because obviously in [Adelaide] we need to be not only physically good, but mentally very good as well."
McCullum and Stokes both
highlighted England's shortcomings with the new ball as a turning point in the game, with McCullum saying they had bowled "terribly" as Australia raced to 130 for 1 in the 21 overs before tea on the second day. "We were trying too hard was my assessment of it," McCullum said.
"We identified that we had a reasonable score with the bat in the first innings, and we knew that there was quite a pivotal moment in the game if we were able to strike. Sometimes, when you do try too hard, you miss your execution, you tighten up, and you're not able to apply the pressure. We're honest with ourselves: we bowled terribly in that period, and Australia were able to canter along at a very strong strike rate."
Stokes held himself and Brydon Carse accountable, saying: "It was myself and Brydon who let all that pressure off. We weren't able to sustain what Jofra [Archer] and Gus [Atkinson] did… Me and Brydon know that we weren't able to back up that first spell, and we weren't able to deliver the consistency that Australia delivered this whole Test match."
McCullum also cited England's fielding as a major issue, after they dropped five catches in the first innings: "It is hard enough taking 10 wickets against a good side like that, let alone needing to take 15. There was areas with the bat where we were deficient, there were areas with the ball where we were deficient, and there were areas in the field where we were deficient."
Matt Roller is a senior correspondent at ESPNcricinfo. @mroller98