The reigning champions withstood a late fightback at Welford Road as they earned a bonus-point victory thanks to a 32-15 scoreline.
"Worcester made it difficult for us," BBC Sport quotes Burke as saying. "They are a good side, they are coached well and they will cause teams a lot of problems this season.
"I am very happy with the bonus point but I am disappointed with our performance at times in the second half."
The Tigers continue the defence of their title on Saturday when they travel to old rivals Bath.