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.
In the other quarter-final fixture on Thursday, Paraguayan outfit Nacional Asuncion play host to Argentina's Arsenal at the Estadio Defensores del Chaco.
Meanwhile, Colombia's Primera A league leaders Atletico Nacional go head-to-head with Uruguayan side Defensor Sporting on Friday.
