The Tigers made sure of a top-four finish on Saturday with a 42-22 victory over Sale Sharks at the Salford City Stadium.
Despite being pleased with his players reaching the playoffs, Cockerill now wants them to push on and be crowned champions for the fourth time in six years.
"It's nice that we've got to this point but we want to win it," he told BBC Sport. "I know everyone's sitting back and saying we're in a semi-final and that's okay considering the (injury) problems we've had - but that's not what we're about.
"We want to still win this and we still think that we can win it and that we're good enough.
"We are still the champions at this point and we haven't been as good as we could have been at some points this year - but we've given ourselves a fighting chance."
Leicester won last season's championship by beating Northampton Saints 37-17 in the final at Twickenham Stadium.