The Brazilian champions face San Lorenzo in the quarter-finals of South America's premier club competition, with the tie kicking off in Argentina on Wednesday.
Cruzeiro made it through to the final eight after accounting for Paraguay's Cerro Porteno 3-1 on aggregate but Oliveira says they will have to better that performance at the Estadio Pedro Bidegain.
"Argentinean football is football very good technically and very competitive," he said.
"Playing at their home, we must have a combination of good things to take there.
"You must have more attention, more than we did in Paraguay."
Oliveira added: "We're going to make a good game, play better and have a strategy specific to this game and try to bring a positive result home."
Cruzeiro, dual Copa Libertadores champions of the tournament, head into the opening leg full of confidence having defeated Atletico PR 3-2 to move level atop of Brazil's Serie A over the weekend.
As for San Lorenzo, they are four points off top spot in Argentina and have only lost one of their past 13 home games in all competitions.
In the other quarter-final fixture on Thursday, Paraguayan outfit Nacional Asuncion play host to Argentina's Arsenal at the Estadio Defensores del Chaco.
Nacional Asuncion, third in the Division Profesional standings, edged Velez Sarsfield 3-2 on aggregate en route to the quarters and are up against Argentinean opposition yet again.
Arsenal beat Union Espanola by a solitary goal to qualify for the next round.
Elsewhere during the week, in-form Lanus of Argentina entertain Bolivar at the Estadio Ciudad de Lanus on Friday.
Lanus are in the midst of a 10-game unbeaten streak on home soil, with nine of those wins, and are up against a Bolivian team that has suffered back-to-back defeats on the road.
Meanwhile, Colombia's Primera A league leaders Atletico Nacional go head-to-head with Uruguayan side Defensor Sporting on Friday.
