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."
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