Manu Tuilagi scored twice in the opening quarter of an hour against the Warriors in the first home game of the new season, and a second successive bonus-point victory followed with further tries from Vereniki Goneva, Graham Kitchener and a penalty try at a close-range scrum.
“We’ve got to be satisfied with two wins and the 10 points first,” said Tigers director of rugby Cockerill .
“We scored five tries again on Saturday and there are lots of positives. I wouldn’t swap it for last year’s start!
“In terms of the performance, though, we know there is still room for a big improvement.
“We did some really good things, but we also gave away a lot of ball and lost field position too cheaply at times. We are creating a lot of opportunities and we need to convert them into scores more often.
“Worcester are a tough side to break down. Last week they were unlucky to lose against Bath and they made us work hard. When we carried and recycled ball properly we were very good but we put ourselves under pressure at times. We know we’ll need to be better than that.”
Tigers have 10 points after scoring five tries in each of the wins over London Welsh and Worcester Warriors, but now prepare for back-to-back matches against the last two Aviva Premiership champions - Saracens at Wembley on Saturday and then at home to Harlequins on September 22.