Cockerill's players overcame Worcester Warriors 34-26 at Welford Road, a week after beating London Welsh away from home, but he was far from happy with the performance even though Tigers scored five tries to Worcester's two.
"It's a perfect start if you look at the table," Cockerill said, "but it was far from perfect performance-wise. But we will take the points.
"We did some really good things and we are creating a huge amount of opportunities but we also turned the ball over too much. We just played ourselves into trouble. It's easily fixed but our mindset needs to be better than that.
"Every time we recycled the ball properly there were opportunities for us. But we were sloppy at times and put ourselves under pressure and that cost us points. We need to be better than that.
"Worcester made us work hard but we should have played better and been more accurate. With the dominance we had in the game, the five tries was a poor return and we need to tighten things up."
Cockerill was delighted with his new Fijian winger Vereniki Goneva and England centre Manu Tuilagi, who scored three of Leicester's five tries between them.
The others came from lock Graham Kitchener and a penalty try.
Tuilagi gave Leicester the perfect start with two tries in the opening 12 minutes and Cockerill said: "Manu has had some criticism but within our structure he plays really well and gets opportunities to run with the ball.
"You saw today his raw power and his ability to make something from nothing. He is still very young but me and (head coach) Matt O'Connor think he will be the best 13 in world rugby in the next 12 months."
Worcester have picked up just one point from their opening two games and played 20 minutes with just 14 men after losing full-back Chris Pennell and scrum-half Shaun Perry to the sin bin.
They scored tries through David Lemi and Alex Grove, with former Leicester fly-half Andy Goode kicking 16 points.
Warriors head coach Richard Hill stressed he is pleased with the progress Worcester are making.
He said: "It was a huge effort on our part today and I can see something building nicely.
"We are bitterly disappointed with the loss. The players are already talking about next weekend because the signs are there and things are better than last season.
"We had the worst possible start being 14-3 down after 12 minutes. We had the ball but they scored two great tries.
"You wouldn't expect to lose tries from that distance and it put us on the back foot. We lost Chris Pennell and Shaun Perry to the sin bin but we showed great character in the way we battled back."
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