Ed Slater and Adam Thompstone scored first-half tries as Tigers led 20-3 approaching the interval but had to survive a Sharks fightback before a penalty try at a close-range scrum helped to close out a 30-23 victory in front of a capacity 24,000-strong crowd at Welford Road.
Fly-half Owen Williams kicked the reaming points with three conversions and three penalties from his six attempts at goal.
“The way we started was very, very good,” said director of rugby Cockerill as Slater and Thompstone dotted down inside the opening 25 minutes.
“We’re creating lots of opportunities to score which is pleasing. But it is a lesson for us – if you get opportunities you take them. You don’t know how many opportunities you’re going to get in a game, so you have to take them.
“We bombed a few chances and left a few tries out there. We turned over ball nine times in their 22 – you score from one of them and you have the bonus-point try.
“I thought we played some really good stuff but, because we didn’t take those opportunities, we let them back in to the game and, credit to Sale, they took their opportunities well.
“But it is a good win and we take the four points.”
The four points kept Tigers in the chase for the top-four spots in the table, four points behind their next opponents, Bath Rugby, who travel to Welford Road on Sunday. Kick-off is at 2pm and tickets are available now.