The reigning champions enjoyed a dominant first-half display that helped them eventually secure a 21-9 win at Sandy Park.
"It was an outstanding effort from our players because Exeter really came at us in the second half," Burke told reporters. "They threw everything at us and not to concede a try today at Sandy Park was good.
"We felt that if we tied Exeter up at the start, got momentum and quietened the crowd down, we would get a foothold in the game. You play in the right areas, get field position, keep hold of the ball and recycle, you will get your rewards.
"I was disappointed that we allowed them to get back into the game in the second half. The scrum was a real force today and we got a lot of rewards out of it."
Leicester host Northampton Saints at Welford Road on Saturday.