After naming a Tigers team which will be led by Martin Corry for the trip to Kingston Park tomorrow (kick-off 3pm), Cockerill said: "Newcastle have had some good results recently, especially at home, and they put 40 points on Sale. We will treat them with utmost respect and we know that if you do not play at the top end of your game then you can struggle.
"Newcastle have been a bit of a bogey team for us in recent seasons - we have lost there in the last two seasons and they got a draw down here last year. You underestimate them at your peril.
"The December-January period has so far gone quite well for us with 12 points from 15 in the last three games. If we win at Newcastle then that would be a very good return from a tough period of the season. So far we are happy, but we want to win every game and Newcastle is the most important game of the season for us now because it is the next game."
Corry has had to deal with the loss of the England captaincy this week, but Cockerill said: "Cozza just came back in and got straight into training. Now he is looking to keep playing well for us and take it from there. He has come back as the same old Cozza and just wants to get back to playing. He will put pressure on Brian Ashton and John Wells and all the players in the England squad for his spot because he plays well for us."
Corry is joined in the Leicester back row by Brett Deacon and Lewis Moody, with Leo Cullen and James Hamilton starting at lock. Alex Moreno, George Chuter and Martin Castrogiovanni make up the front row as Tigers look to tighten their hold on a place in the top two places in the Guinness Premiership.
Harry Ellis and Andy Goode return as the half-back pairing, with Sam Vesty moving to centre alongside Ollie Smith who is in line for his 150th Tigers appearance. Leon Lloyd is on one wing and Seru Rabeni makes his first start since the opening month of the season on the other. Johne Murphy is at full-back.
Daryl Gibson, who is recovering from an Achilles injury, has been named on the bench.
"Daryl will will play some part of the game," said Cockerill. "He is very important in terms of a leadership and also from a playing point of view."