Cockerill's team face Heineken Cup Pool Four rivals Clermont Auvergne at Stade Marcel Michelin, where victory would see them take a giant stride towards achieving quarter-final status.
Leicester are unbeaten in their last seven matches, and they are buoyed this weekend by the return after injury of England internationals Manu Tuilagi and Tom Croft.
"We've beaten Ulster, beaten Gloucester away, then Northampton, and now we've got Clermont home and away. That is the toughest five weeks in a long time," Cockerill said. "They are all intense games.
"You take your bumps and bruises, but you have to recover quickly. You get back to training, get back to working hard and get on with preparing for the next game. But it helps that process when you are winning games too.
"We had a good win last week in an emotionally-intense game (against Northampton). It was a classic local derby which either side could have won in the end.
"If you have a poor period in a game you can let good sides back in. We have done that a few times recently and we've got to cut that out, but we are getting better."
As an ex-Clermont player, former England hooker Cockerill is in a good position to anticipate what is coming Leicester's way on Sunday.
"There will be a full house and lots of noise," he added. "The rugby club is right at the heart of the city, and they will want to welcome Leicester Tigers on and off the field.
"They are a quality team, with quality throughout the whole squad. They have the best attack and the second-best defence this season in the French league.
"It is a huge challenge for us, but we will go there and enjoy the battle. We've got to give it our best shot."
Nathan Hines, meanwhile, has no doubt which parts of Clermont's game will need to be in pristine condition when they greet Leicester.
Former Scotland lock Hines features in a Clermont line-up that cannot afford any further Pool Four setbacks following their defeat against Ulster last month.
"People say Leicester have had a rough time in the Premiership recently, but the signs are there that they have started to sort that out and their pedigree in the Heineken Cup is understood by everyone in the competition," Hines said.
"And, more than any other side you play against, you have to have the tools to do the job against Leicester.
"That means you have to have a strong scrum and lineout because they always have powerful set-pieces.
"Unlike the Premiership and the (French) Top 14, you can make amends for a bad performance or bad result during the course of a season. In the Heineken Cup, the next two weeks decide your fate.
"There is a pressure there, and it's such an unforgiving competition now. You can win a game, but fail to get a bonus point, and you are out of the Heineken Cup."
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.