Marcelo Gallardo said River Plate "cannot play worse" with a Copa Libertadores semi-final berth at stake.
River travel to the Estadio Governador Magalhaes Pinto in Belo Horizonte on Wednesday, trailing Brazilian champions Cruzeiro 1-0 following last week's quarter-final clash in Buenos Aires.
Gallardo's River enjoyed the better opportunities and were unfortunate to walk away empty-handed as Cruzeiro left the Argentine capital with a priceless away goal courtesy of Marquinhos.
But Gallardo has not given up home of steering River to the final four of CONMEBOL's premier club tournament.
"We cannot play worse than this game," Gallardo said following the first leg.
"Now we have the possibility of going to beat [Cruzeiro in] Brazil and as long as that chance [remains], this team never gives up for dead.
"This is what we have left to win, we have to play better, with greater determination and resolve."
Dairon Mosquera's 92nd-minute goal lifted Santa Fe past the Brazilians last week and the Colombia outfit are aware of the task ahead at the Estadio Jose Pinheiro Borda in Porto Alegre.
"We were reassured by the victory but we know we must be very concentrated for the return game," said Santa Fe coach Gustavo Costas.
"Brazilians at home will always be harder. But we have an advantage and we want to keep it and, if possible, enlarge it."
On Tuesday, Ecuador's Emelec make the trip to Mexico with a one-goal lead up their sleeve against Tigres UANL.
Racing Club and Guarani complete the quarter-final fixtures in Argentina on Thursday - the latter holding a narrow advantage following last week's triumph in Paraguay.
