Ukraine coach Oleg Blokhin was relieved to see his side make the knock-out stages after they beat 10-man Tunisia 1-0 in Berlin on Friday.
"It was a tight game, a question of nerves," he said. "We had chances but we didn't take full advantage.
"After the sending-off, the players probably took it a bit too easy - the Tunisians started moving about causing us problems.
"I was nervous until the very end. Now I'm very satisfied."
He added: "Maybe we took it too easy at first and Tunisia really confounded us with a lot of difficult situations, but when we scored then we became the superior team."
We always kept our belief despite the terrible defeat against Spain
Andriy Shevchenko got Ukraine's only goal from the penalty spot after 70 minutes - with Tunisia having had Ziad Jaziri sent off - to secure their passage in their World Cup finals debut.
It is a fine achievement for a side who started the tournament with a 4-0 drubbing at the hands of Spain.
Shevchenko added: "It's a hugely important achievement for Ukrainian football that we have got into the next round.
"We always kept our belief despite the terrible defeat against Spain.
"It doesn't matter who we play in the next round. All three teams - France, Switzerland and South Korea - are strong teams."