The 26-year-old, who finished the World Cup as England's first-choice fly-half, has been sidelined since New Year's Day with a knee injury but returned to help defeat his former club 24-13 and put himself in contention to face Italy on February 11.
There was further good news with Cockerill confirming centre Manu Tuilagi was due back in full training this week but lock Louis Deacon's season looks over.
Tigers director of rugby said: "We got Craig Newby and Toby Flood back on the field, but it was always going to be a difficult game.
"Toby will go and train with England early next week, and it is up to Stuart Lancaster to decide if he wants him to stay with them or to let him play for us over the next couple of weeks.
"Manu Tuilagi will have a full training week this week, and should be available for selection next weekend against Exeter. Louis Deacon's season, unfortunately, might be over.
"It was a muted crowd and a bit of a muted performance, but it is a case of job done.
"Newcastle are trying to build a side and a game-plan, but the penalty count was horrendously against them and they were probably fortunate to receive only one yellow card."
Leicester will face either Saracens or Bath, with their fate decided by Sunday's games, while Newcastle director of rugby Gary Gold was left to turn his attention to next week's Aviva Premiership clash with Bath.
"It was a useful run, and we got a couple of guys back from injury in time for the Premiership return at Bath next weekend," he said.
"Regardless of the competition we are never going to play a game of rugby and not compete, and we showed good character.
"Leicester are one of the top teams, and it shows there is still a lot of work to be done.
"We never gave up, and I am proud of the guys for sticking in there in the second half.
"The conditions were obviously not great, but they were the same for both teams."
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