Cruzeiro, River Plate, Internacional, Santa Fe, Emelec, Racing Club, Emelec and Tigres UANL are all vying for a spot in the semi-finals.
Marcelo Oliveira wants to see improvement from Cruzeiro as the Brazilian champions prepare to travel to Argentina for the opening leg of the Copa Libertadores quarter-finals.
Cruzeiro are on the road in Buenos Aires on Thursday, tackling Argentine Primera Division winners River Plate, who advanced to the quarters following CONMEBOL's decision to expel Boca Juniors from the competition after rival players were sprayed with an irritant substance.
With the field for the last eight confirmed and Cruzeiro's opponents decided, Oliveira turned his attention to Thursday's first leg and said his team must improve in the final third.
"We have to be different on fighting spirit, competitiveness and also have to attack more," Oliveira was quoted as saying on Cruzeiro's website following Sunday's 1-0 loss to Santos in the Brazilian Serie A.
"We think to do this in this game. Now we have resolved the issue and we know we will face the River, which is a very traditional and successful club. We have to be more efficient."
Cruzeiro earned their spot in the quarters after edging Brazilian rivals Sao Paulo on penalties, while River were awarded a 3-0 win as a result of the crowd violence at Boca.
"Against Sao Paulo, when we were quite combative, organised and played well with and without the ball," Oliveira added.
"We did what we had to do and tried to repeat it today [Sunday], but unfortunately did not work out. I hope that on Thursday it is a different story.
Guarani against Argentine outfit Racing Club in Paraguay is the other fixture scheduled on Thursday.
Fernando Jubero's Guarani stunned Corinthians 3-0 on aggregate in the round of 16, a day before Racing overcame Wanderers 3-2 over two legs.
Colombia's Santa Fe host Internacional at Estadio Nemesio Camacho in Bogota on Wednesday.
Midfielder Vitinho is expected to be reinstated to Inter's starting line-up, having come off the bench on Sunday, while he missed the club's second-leg win over Atletico Mineiro.
"Every player goes through tough times, not just me," said the Brazilian. "I see progress and [coach Diego] Aguirre is pleased with my workouts. I kept my focus, I kept quiet and I knew things were going to work."
Emelec of Ecuador and Mexico's Tigres UANL kick-off the first-leg fixtures in Manta on Tuesday.