McCann's men beat the Highland League champions 2-0 at Dens Park but the manager was less than impressed by the performance.
"The attitude just wasn't there and it was so unlike what we've been seeing up until now," he said.
"I cancelled their day off because we were so poor overall."
Goals in each half from Faissal El Bakhtaoui and Sofien Moussa secured victory for Dee in the Group C match on Saturday.
But McCann expects much better in the upcoming League Cup matches against Cowdenbeath and Dundee United, with the Dens men starting their Premiership campaign at home to Ross County on 5 August.
"There were only a few with pass marks after that performance," he said. "It's hard to explain where that came from and I don't think it was so much to do with disrespecting the opposition.
"You only get what you deserve in this game and we'll speak about why it was like that on Saturday.
"We can't stroll about like that and think we're going to win a game outright just because we're a Premiership team.
"It doesn't work like that in football and they know that."
Dundee boss Neil McCann cancelled his players' planned day off after their below-par showing in the League Cup against Buckie Thistle.