Twelvetrees scored two tries, both of which he converted, and five penalties as Tigers overcame a slow start to eventually overwhelm a doughty Wasps side.
Cockerill praised the rapid development of 23-year-old Twelvetrees, who prefers to play at inside centre but stepped into the fly-half role in place of the injured Toby Flood.
"Billy has improved this year out of sight," Cockerill said.
"His ball-carrying has been really good for us and, as you saw, his goal-kicking was very, very good."
Twelvetrees was playing inside Anthony Allen, who has only just returned from a long-term injury, and the combination took some time to bed in as Wasps took an early lead and threatened to push Tigers even harder.
"Billy was a bit rusty at 10 because he's not played there for a little while, and Anthony Allen at 12 hadn't played for three months, so that combination was a little bit rusty," Cockerill said.
"It was a little bit laboured but you have to give credit to Wasps.
"They defended very, very well. We tried to play and they came to disrupt and get in among us."
Twelvetrees admitted that, despite his 29-point haul, he was not at his best.
"My overall game at 10 was a little bit rusty, and we weren't very fluent in the first half, but in the second half we brought a different intensity," Twelvetrees said.
"The forwards started to dominate and that makes it easier for any number 10."
But he played down talk of an England call-up, saying: "For me it's just about helping Leicester out and playing well in the Leicester shirt."
Wasps director of rugby Dai Young was pleased with his side's defensive effort but admitted they had come against a team with more firepower.
"Some of our defence was heroic," Young said, "but you can't spend the amount of time defending that we did against a side like that.
"We were certainly in the game in the first half, and we had one or two opportunities to put some distance between ourselves and the Tigers.
"Unfortunately when we did get in the right areas a line-out went astray or we gave a couple of penalties away.
"When you're scrapping and need a little bit of luck, things just don't go your way."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.