A scrappy 1-0 win over Tunisia on Friday earned the Ukrainians a second-round match against Group G winners Switzerland, and although coach Oleg Blokhin was satisfied with the result, he was unhappy about the quality of the football.
He said his team needed to do some serious thinking before Monday's match in Cologne but was hopeful that Ukraine could progress to the quarter-finals.
"Chances always die last," he told reporters.
But to get any further they will need to do what no other team has managed in the tournament so far -- score against Switzerland, the only side yet to concede a goal.
That job will fall to striker Andriy Shevchenko, European Footballer of the Year in 2004.
Shevchenko is by far the team's most skilful and well known player, but Blokhin said football was all about the team rather than individuals.
"I don't ever single out one player (for praise or criticism) -- the team either wins or loses," Blokhin said.
The first European team to qualify for the finals, the Ukrainians came to Germany viewed as the dark horses.
A 4-0 loss to group winners Spain raised questions about that, although they answered critics with a 4-0 win over Saudi Arabia.
Even if Ukraine are knocked out on Monday, the team will still be pleased with their World Cup debut.
"It's the first time Ukraine have got to the tournament, the first time Ukraine have qualified from the group. I congratulate the whole of Ukraine, especially the fans, with this big achievement," Blokhin said.
