The Ukrainian outfit are into the last eight having advanced past Ajax on away goals, after their tie finished 2-2 on aggregate.
Dnipro's Europa League campaign began in underwhelming fashion, with a first-up win over Hajduk Split in a play-off followed by four goalless performances - including a home loss to Qarabag in the group stages.
Markevych's men managed to reach the knockout rounds by winning the reverse fixture at Qarabag, and also downing Saint-Etienne at home - before seeing off Olympiacos in the last 32, and the Eredivisie powerhouses in the round of 16.
The 64-year-old tactician said he was putting no limit on his side's potential, and said they can break Dnipro's European trophy drought.
"I have not wavered in my opinion that we cannot win the Europa League," Markevych said.
"That said, nobody believed we could reach the quarter-finals and here we are.
"The mentality and courage of the team is crucial for us, and the players must once again give their all.
"Tomorrow is part one and only in Kiev will everything be decided."
Markevych added, on Thursday's hosts at the Jan Breydel Stadion: "Club Brugge have a very intense style, they are very strong at the back and play very compactly, always trying to squeeze their opponents.
"They have not lost a single match in the Europa League so we will have to be at our best.
"For me it's the same game home or away: we will not adjust our strategy for that."
