The Swans were outmuscled at the stoppages by the Lions on their way to a 33-point loss at the Gabba and the manner of the defeat clearly rankled with McVeigh.
"We were embarrassed with our performance. We want to really stick to our trademark as a footy club and that's hard, contested footy," he said at a joint press conference with Carlton skipper Chris Judd on Tuesday.
"We were soft on the weekend and [we're] having a good hard look at ourselves this week. It starts today at training and we'll be ready to go this week and hopefully you'll see a different team."
McVeigh said the Swans would continue aspiring to be one of the hardest "one-on-one" sides in the competition, but he conceded that their hard-won reputation could be easily compromised.
"I guess it can happen in a year of footy. We do think we are respected in that area and that's what we've prided ourselves on for the last seven years. We'll be continuing that and driving the players to be exemplary in that area," he said.
Judd, who spoke with the Sydney football media via video link to promote Saturday afternoon's clash at the SCG, was in no doubt that the Swans remained among the AFL's elite teams when it came to winning the contested ball.
He cited the Swans' strong win against Hawthorn in round two and predicted their stoppage-friendly style of footy would test his midfield teammates at Carlton.
"Sydney still sit very high in our estimates and they're going to be a great test for us, and particularly for our younger players, who haven't played in the style of game which Sydney forces you to play," Judd said.
"It's always pretty congested around the footy and playing on a small ground like the SCG, it exposes our players to a different style of footy.
"It's a style of footy that you often come up against in finals, so it's a learning experience for us."
The Swans will be out to extend Carlton's 16-year losing streak in the harbour city when the two teams meet in the Swans' first-ever Saturday afternoon home game.
The Blues last triumphed in Sydney in round seven, 1993, when a team featuring Craig Bradley, Stephen Kernahan, Justin Madden and Tom Alvin prevailed by 44 points.
"The Carlton community is full of these sorts of statistics that we really need to break to form that winning culture," Judd said of the club's long losing streak in Sydney.
"They're one of the best one-on-one sides to have played in the modern era and we're looking forward to testing ourselves up there against the Swans."
