Lake had a poor third quarter and was on Monday referred directly to the AFL Tribunal for an incident involving opponent Drew Petrie.
But there were several moments of poor discipline from the Hawks during the third term as the Kangaroos quickly turned a four-point deficit into a 35-point lead.
Burgoyne said Hawthorn's on-field discipline had been good before the North match and the players had spoken in the past few weeks about not going too far.
"It was unacceptable, but it's pretty unfair just to point it single-handedly at Brian," Burgoyne said of their full-back behaviour.
"We had a number of players give away free kicks in that time (and) that reflects poorly on the team.
"We like playing on the edge - we think that's when we play our best footy - when we're playing right on the edge, but not giving away those free kicks and overstepping the mark.
"Then it takes away (from) what you're trying to do.
"You're just giving the opposition a free run, a free kick and they obviously get a bit of momentum."
The most galling feature for Hawthorn about North's six-goal surge in the third term was that the Hawks only lost by 20 points.
"We lost our way there for a good 10 or so minutes, where they were able to pile on some good scoreboard pressure and we weren't able to stem that," Burgoyne said.
"That (Lake's wrestle with Petrie) was one incident, but there were a few other incidents after that, that cost us.
"As a team, that was unacceptable."
Lake's referral to the Tribunal continues a tumultuous premiership defence for Hawthorn.
The Hawks’ succession of injuries continued on Friday night when Bradley Hill (knee) was a late withdrawal and Brad Sewell suffered another hamstring injury.
The loss was also the first game back for Clarkson after his five-game absence because of a serious illness.
"I can't think of another year like this," admitted Burgoyne, who is a 259-game veteran.
Hawthorn faces another test on Friday night when it heads to Adelaide to play the resurgent Crows, who are closing in on the top eight.
In round 10, the noise was deafening at Adelaide Oval when Port beat the Hawks by 14 points.
"We know it's going be 50,000-plus Adelaide fans going nuts," Burgoyne said.
