Considered one of the outside favourites entering the World Cup, Belgium claimed three wins in Group H without being overly impressive, also beating Algeria and Russia to set up a date with the USA in the round of 16.
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"Yet again our patient approach paid off," Wilmots said.
"I knew that the Koreans would leave us with a lot of space to play with. My young team had a tendency to push forwards too much at times, so I tried to get them to relax a little.
"It’s no easy task to finish the group stage with nine points. It’s a truly historic achievement for Belgium, and I’d like to congratulate the staff and all the players.
"We're here to win, not to play beautiful football, and we've accomplished our mission."
Defender Jan Vertonghen scored the match-winning goal in the 78th minute at the Arena Corinthians in Sao Paulo, despite midfielder Steven Defour's red card just before half-time for a reckless, studs-up challenge.
And the Tottenham centre-back was delighted, particularly with his side's ability to claim a win with only 10 men.
"After scoring, I wanted to share my indescribable joy with our supporters. We feel like they’re really behind us, and that’s important for the squad," Vertonghen said.
"Finishing top of the group and pulling off a late win with 10 men is also a real source of satisfaction."