Tigers bounced back from last week's humiliating 38-0 Champions Cup loss in Munster by winning the return game 18-16 thanks to a late Owen Williams kick.
Cockerill told BBC Radio Leicester: "Is that a team that plays for a coaching group that doesn't work?
"They are playing for everybody."
Williams' long-distance 79th-minute penalty means Leicester remain in contention to qualify from Pool One of the Champions Cup. Glasgow top the group following their victory over Racing, with Munster on 11 points and Tigers third on eight points.
Cockerill, who called the defeat against Munster at Thomond Park "unacceptable", said the coaching set-up at Welford Road had a "robust" relationship that was normal.
But the 45-year-old was defiant when responding to reports his near eight-year spell in charge of Leicester is coming to an end.
"If you don't lose so heavily in Munster it doesn't get questioned," he added. "Is it all fixed tonight because we won? Well, we kicked a penalty in the 79th minute from 52 metres. Does that make everything right and there are no problems?
"We don't agree on everything. Newsflash: that is the coaching team and that is what we are here for. Different opinions on how you want to play is a healthy thing.
"We will always have different ways of doing things and sometimes we will play badly."
Cockerill has been in charge of Leicester since January 2009 and is in no doubt he should stay on.
"I think I am a strong leader and I lead from the front," Cockerill said. "Some people like me and some don't and I don't really care because at Leicester you are either in or out.
"If you're in then great and there are a lot of people here tonight who are in. I'm in here for the battle until someone tells me I am not here for the battle.
"I have been here a long time. That doesn't mean I should stay here but I want to be here because I think I do a good job. Who's going to do a better job than me?"
Long-serving director of rugby Richard Cockerill has said reports claiming he faces the sack and that describe the coaching structure at Leicester Tigers as toxic are "rubbish".