The Tigers notched up their second consecutive bonus-point win of the campaign on Saturday when they defeated Worcester Warriors 34-26 at Welford Road.
However, Cockerill believes that his side still needs to sharpen up in order to avoid losses down the line.
"It's a perfect start if you look at the table, but it was far from perfect performance-wise," he told Sky Sports News. "But we will take the points.
"It's easily fixed but our mindset needs to be better than that. We were sloppy at times and put ourselves under pressure and that cost us points. We need to be better than that."
The win has put Leicester third in the Aviva Premiership table.