The Swans recorded their lowest contested possession count for the season (138) in the 37-point loss and gave the Hawks too much freedom when they had the ball, particularly early.
McVeigh said it was an out of character performance for the Swans, who average a League-high 158 contested possessions a game and are also ranked top five for tackles.
"It started with our hardness, and we like to base our game on that. " McVeigh told AFL.com.au.
"They were a lot harder than us and then when we did win the ball our kicking to our forwards and around the ground was terrible.
"You can't do that against a good side like Hawthorn because they make you pay the other way."
McVeigh, who had 19 disposals on Saturday night, was one of several Swans midfielders off the boil, with Dan Hannebery (19 disposals), Ryan O'Keefe (18), Jude Bolton (15) and Luke Parker (19) all quiet.
Adam Goodes (27 possessions and 10 inside 50s) and Josh Kennedy (30 and 13 clearances) led the way, and McVeigh said more Swans midfielders needed to jump onboard.
"They (Hawthorn) were on top in that area and had a lot more of the footy than us," he said.
"We weren't getting the ball and we couldn't stop their influence.
"Our midfielders have been in pretty good form over the first half of the season, but they've got a lot of good mids as well.
"The competition steps up and Hawthorn stepped up and we didn't in a big game when it counted."
Nathan Schmook is a reporter for AFL Media. Follow him on Twitter: @AFL_Nathan
