"All we can do is keep emphasizing it," he said Friday after a 19-11 win over the Alouettes in Montreal.
"(But) sooner or later, we'll have to put different people in different positions. We certainly can't turn the ball over late in the game like that, or almost turn it over late in the game. That was probably the scariest one of all."
Burke was referring to Jovon Johnson's fumble of a kickoff in the fourth that was pounced on by teammate Bryant Turner before it fell into the wrong hands.
The Bombers (1-1) turned the ball over five times on Thursday, three times in the first quarter alone. Turnovers were also a major factor in Winnipeg's 38-33 home opener loss to Montreal the week before.
In addition to reducing turnovers, Burke says the Bombers have to find a way to defend against the blitz that hampered their offence. Pierce was sacked five times.
"We're going to have to come up with an answer for that or we'll see the blitzing every week," he said.
Montreal quarterback Anthony Calvillo had it even worse. He was sacked seven times as Winnipeg's defence stymied the Alouettes new, no-huddle offence.
Turner, who has developed into one of the most reliable players on the Bomber defence, had to stay behind at a Montreal hospital for observation after the game. Burke says initial tests turned up nothing but they will know more in a day or so.
"They didn't really find anything significant," Burke said. "They just kept him there overnight to make sure he's OK."
Turner, in his third season with the Bombers and tied for the CFL lead in sacks already with three in just two games, appeared to have difficulty breathing in the fourth. He was given oxygen on the field.
Overall, the biggest factor in the win Thursday appeared to be Winnipeg's strong defence that kept Calvillo from getting past the Bomber goal line most of the night.
Burke, a former defensive co-ordinator, made it clear in training camp he wanted a lot more from the Winnipeg defence, in particular the secondary.
Veteran Jonathan Hefney was released when he failed to measure up and the tough love approach seems to have worked, with the defence looking more like that of Bomber editions past. Winnipeg built a reputation for itself in the CFL as a tough defensive team.
"Great effort," said Burke. "Guys were very solid up front with pressure on the quarterback and the secondary was very good at not giving up any big plays. I'm really happy with those guys."
Burke said overall he was happy with the effort shown on both sides of the ball.
Pierce agreed they have to find a way to stop the turnovers but he took positives out of the way the offence hung in there, even capitalizing on the blitz that left receiver Cory Watson open at times.
"A tipped pass, deep in your own territory, and it gets picked off, those things are going to happen," said Pierce.
"You have to be able to fight through that and be mentally tough. We were pinned down and last week we couldn't get out of our own zone and (this week) we made a big play to Cory and got out of our zone and put together a 105-yard-drive right there.
"Those are things we're capable of. We've got to continue to work at it and put it all together."